Ok, A few Ideas:
1, could be injectors try putting a bottle of injector cleaner in the tank.
2, E38's have a problem with oil getting around the back two spark plugs, due to the camber of the engine ( leans back ) ,the oil comes from the rocker cover gaskets & rubber seals around the bolts, this happens over time (dont know your mileage?)
3, Idle valve dirty
4, could be your fuel pump
I would go with the injector cleaner 1st and see what happens, may take a couple of days to work its self through the system, bung the whole bottle in on nearly empty tank then fill up( ignore what it says on the bottle) Then get back to me via PM and we an go from there, as Im in the UK dont expect an instant response due to time zones
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