B757-200
Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Critical
Flight Crew Inflight Shutdown; Flight Crew Returned To Departure Airport; Flight Crew Landed in Emergency Condition
Aircraft
While climbing out of ZZZ at approximately 10;900 feet; we heard a loud bang and the aircraft yawed.  Master caution lights and EICAS messages EEC OFF and RT ENG LIMITER illuminated. Followed QRH procedure.  Declared an emergency and returned to ZZZ for an overweight landing.  Touchdown was smooth and brakes were not applied till 70kts.  Brake temperatures were checked by AARFF and we were cleared to the gate.  Passengers deplaned normally via the jet bridge.  Entered the discrepancies and overweight landing in the logbook.
B757-200 Captain reported engine failure after takeoff. Flight returned to departure airport.