I'm reluctant to add to the above because I don't know the 737 architecture but I'll offer that on the 777, which I'm guessing might possibly have vaguely similar plumbing, the Fuel imbalance checklist ( which you may well have to action post an engine failure) involves opening a crossfeed and then turning off the fuel pumps in the (wing) tank containing the least fuel.. as a result the live engine burns fuel from the "high" quantity tank until such time as you decide to stop balancing.
Any chance the 737 architecture is similar and would allow the same sort of procedure...? It should all be made clear in the FCOM/QRH and Flight Crew Training Manual.
(beaten to it by BPK....)
Last edited by wiggy; 14th April 2019 at 17:51.