77E must be the internal BA code denoting the exact configuration planned to operate your flight.

It seems that there's been some recent change in MMB so that it now shows this when the aircraft has been allocated to the flight, although it has long been visible in (eg) EF from the time the flight is edited at T-3d. I imagine that your return flight still only shows the generic "777" because it's too far out at this stage. (For these purposes, "77W" is also usually a generic code when you see it, as it's the standard IATA code for the 777-300ER.)

See this thread for a bit more: http://www.flyertalk.com/forum/briti...raft-type.html