ThreeTenABP
The other answers are correct, but outdated before they were written. These days I recommend you use the modern Java date and time API known as JSR-310 or java.time. Your date-time string format is ISO 8601, which the modern classes “understand” as their default.
Can you use the modern API on Android yet? Most certainly! The JSR-310 classes have been backported to Android in the ThreeTenABP project. All the details are in this question: How to use ThreeTenABP in Android Project.
long epochTime = OffsetDateTime.parse("2017-09-10T18:35:00+05:00")
.toInstant()
.getEpochSecond();
The result is 1505050500.
Edit: Arvind Kumar Avinash correctly points out in a comment: You do not need to convert an OffsetDateTime to an Instant to get the epoch seconds. You can simply use OffsetDateTime#toEpochSecond.
Example of how to convert this into a human-readable date and time:
String formattedDateTime = Instant.ofEpochSecond(epochTime)
.atZone(ZoneId.of("Africa/Lusaka"))
.format(DateTimeFormatter.ofPattern("EEE, d MMMM h:mm a", Locale.ENGLISH));
This produces Sun, 10 September 3:35 PM. Please provide the correct region and city for the time zone ID you want. If you want to rely on the device’s time zone setting, use ZoneId.systemDefault(). See the documentation of DateTimeFormatter.ofPattern() for the letters you may use in the format pattern string, or use DateTimeFormatter.ofLocalizedDateTime() for one of your locale’s default formats.