His brother Simon gives you the quest My Dead Brother where he wants you to find Edgar's corpse in the Lair of Infinite Agony so he can kill him again. He puts a curse on you, that while very look, will kill you in a week (not really but story).
Edgar seems to be more mellow and very laid back. He commands the powers of Fire.
Edgar will try to get you to side with him and attack Simon.
Siding with Edgar will get you a Blue Assault Rifle.