I recently needed to transfer an app from my eDGe for which I didn't have APK anymore from which I installed it.

To get the APK for an app installed on your eDGe, do the following:
- launch ES File Explorer (under Applications)
- press the Menu button and pick "Manager" then "App Manager"
- tap and hold the app you want to back up and pick "Backup"
- the backup will be made, and a brief message displayed near the bottom of the screen where the APK has been placed (default is "/sdcard/backups/apps" in ES File Manager, equivalent to "Internal Storage" - "backups" - "apps" in the Storage app)

The APK you can now send to another device, copy to your external SD card, upload to DropBox, email, etc.