How to remove a failed Edge Transport

Open Command prompt with elevated privileges

Browse to location C:\Windows\ADAM
Type ADAMUninstall /i:MSExchange and hit enter
Click Yes on both the dialog boxes appearing after you hit enter
Restart the server
While you reinstall the exchange edge transport role, you may receive some weird errors at the first time. This is expected to happen when you remove everything in a crude way.

Locate the registry key HKLM\SOFTWARE\Microsoft\ExchangeServer\V14\EdgeTransportRole
Delete the WaterMark string from the right hand side pane of registry editor
Browse back to location HKLM\SOFTWARE\Microsoft\ExchangeServer\V14\
Right click and create a new key named Transport
Create one more key named Pickup at HKLM\SOFTWARE\Microsoft\ExchangeServer\V14\
Re-run exchange edge transport setup
Your edge transport role should be back to operation and you can create a new edge subscription with Exchange 2013 mailbox or Exchange 2010 HT servers.