Perhaps some techy types could give us some figures about the time taken to replace an engine, as opposed to testing and replacing internal parts.
Depending on the operator and engine (777 engines, due to their size, tend to take a little longer), an engine change is somewhere between 8 and 24 hours. Some operators routinely do engine swaps during an overnight.
I've never heard of an operator opening up an engine core 'on wing', in a shop it's typically a few weeks, depending on the extent of the work. The newer engines can be broken into modules - fan module, compressor module, hot section module, that sort of thing. If only one module needs work, they'll replace that module (day or two) and return the engine to service while the module in question will go into the shop for overhaul.
If the operator doesn't have an available spare, the engine manufacture typically has several 'lease pool' engines available as spares (although it may take a couple days and a very expensive Antonov charter to get it to where its needed).