Briefly, and in a very general sense as I was WE and cannot speak for the specifics of ME or AE, the engineering officer concerned will consult with system senior rate technician, (artificer when I was in).
He will ask the senior rate to outline the problem, the solution and time to resolve.
He will then brief the command on the situation and help assess the effect on the ship's operational capability.
He may well have multiple other situatuations to deal with at the same time.
What he won't be able to do is get stuck in to the engineering problem/solution.
That's what the system technicians are for.
Like I said though, that's very general and each situation will vary, requiring a slightly different approach.
As an Engineer Officer: true dit. The biggest requirement for engineering knowledge is drafting the OPDEF line 5!