A Study to Evaluate the Efficacy and Safety of E2086 in Adults With Narcolepsy

Inclusion Criteria: Participants must meet all of the following criteria to be included in this study: 1. Male or female, age greater than or equal to (\>=) 18 years (or as regionally appropriate) at the time of informed consent 2. NT1 Cohort: Must fulfill Inclusion Criteria 2a and 2b 1. Diagnosis of NT1 within the last 10 years of screening, as confirmed by at least one of the following: * Polysomnography (PSG) and Multiple Sleep Latency Test (MSLT) results, and clinical history, consistent with the 2023 International Classification of Sleep Disorders, 3rd edition, text revision (ICSD-3-TR) criteria for NT1 * Cerebrospinal fluid orexin-A/hypocretin-1 concentration less than or equal to (\<=) 110 picograms per milliliter (pg/mL) 2. At least 4 or more episodes of cataplexy/week as averaged over 2 weeks minimum and confirmed by the cataplexy portion of the Diary If PSG or MSLT results are not available within the last 10 years of screening to fulfill Criterion 2a then screening assessment results for PSG or MSLT can be used instead 3. NT2 Cohort: Diagnosis of NT2 within the last 10 years of screening, as confirmed by PSG and MSLT results, and clinical history, consistent with the 2023 ICSD-3-TR criteria for NT2 If PSG or MSLT results are not available within the last 10 years of screening to fulfill Criterion 3 then screening assessment results for PSG or MSLT can be used instead 4. ESS score \>=10 5. Reports regular bedtime, defined as the time that the participant attempts to sleep, between 22:00 and 01:00 (based on data from the screening Diary) 6. Reports regular waketime, defined at the time the participant gets out of bed for the day, between 05:00 and 10:00 (based on data from the screening Diary) 7. Reports being in bed between 7 and 9 hours per night (based on data from the sleep portion of the Diary) 8. Compliance rate \>=80 percentage (%) for completion of the Diary during screening 9. Body mass index (BMI) \>=18 to less than (\<) 35 kilograms per square meter (kg/m\^2) at Screening Exclusion Criteria: 1. Females who are breastfeeding or pregnant at Screening or Baseline (as documented by a positive beta-human chorionic gonadotropin \[ß-hCG\] (or human chorionic gonadotropin \[hCG\]) test with a minimum sensitivity of 25 international units per liter (IU/L) or equivalent units of ß-hCG \[or hCG\]). A separate baseline assessment is required if a negative screening pregnancy test was obtained more than 72 hours before the first dose of study drug 2. Females of childbearing potential who: * Within 28 days before study entry, did not use a highly effective method of contraception, which includes any of the following: 1. total abstinence (if it is their preferred and usual lifestyle) 2. an intrauterine device or intrauterine hormone-releasing system (IUS) 3. a contraceptive implant 4. Combined estrogen and progestogen-containing hormonal contraception (oral, intravaginal, transdermal) or progestogen-only hormonal contraception associated with inhibition of ovulation, such as desogestrel (oral, injectable). Participants using hormonal contraceptives must be on a stable dose of the same contraceptive product for at least 28 days before dosing, throughout the study and for at least 28 days following study drug discontinuation 5. have a vasectomized partner with confirmed azoospermia * Do not agree to use a highly effective method of contraception (as described above) throughout the entire study period and for 28 days after study drug discontinuation. Participants on an oral contraceptive must use an additional study method throughout the study and for 28 days after study drug discontinuation. For sites outside of Europe, it is permissible that if a highly effective method of contraception is not appropriate or acceptable to the participant, then the participant must agree to use a medically acceptable method of contraception, that is, double-barrier methods of contraception such as latex or synthetic condom plus diaphragm or cervical/vault cap with spermicide. NOTE: All females will be considered to be of childbearing potential unless they are postmenopausal (amenorrheic for at least 12 consecutive months, in the appropriate age group, and without other known or suspected cause) or have been sterilized surgically (that is, bilateral tubal ligation, total hysterectomy, or bilateral oophorectomy, all with surgery at least 1 month before dosing). 3. Clinically significant illness that requires medical treatment within 8 weeks of dosing or a clinically significant infection that requires medical treatment within 4 weeks of dosing 4. Evidence of disease that may influence the outcome of the study within 4 weeks before dosing (for example, psychiatric disorders and disorders of the gastrointestinal tract, liver, kidney, respiratory system, endocrine system, hematological system, neurological system, or cardiovascular system) 5. Any history of surgery that may affect PK profiles of E2086 (for example, hepatectomy, nephrectomy, digestive organ resection) or who have a congenital abnormality in metabolism at Screening 6. Any clinically abnormal symptom or organ impairment found by medical history at Screening, including severe renal impairment (estimated glomerular filtration rate \[eGFR\] \<30 milliliters per minute (mL/min), and physical examinations, vital signs, ECG findings, or laboratory test results that require medical treatment at Screening or Baseline 7. A prolonged QTc interval calculated using Fridericia's formula (QTcF) greater than 450 milliseconds (ms) according to central reading at Screening or Baseline. If the QTcF machine read is greater than 450 ms on the first single 12-lead ECG, 2 additional 12-lead ECGs will be performed 1 minute apart and the mean of the 3 QTcF values will be calculated 8. Persistent systolic BP greater than (\>) 130 or \<100 millimeters of mercury (mmHg) or diastolic BP \>85 or \<50 mmHg a