Being a large Corps (and one that is reknowed for 'empire building') there is a huge range of things that you could end up doing. Your trade, however, is unlikely to be one of them. Unless you are a Resources Specialist, Driver or Signaller, Combat Engineering will probably consume far more of your time than whatever your trade is.
It's pretty hard to generalise as to what your average Sapper gets up to on Ops - it could be anything from building a NAAFI to breaching a minefield to being part of a counter-terrorist search team to deploying as second-line infantry etc etc etc.
Promotion is pretty slow in the Corps compared to some other capbadges but opportunities to specialise open up as you go up the ladder. Your normal day-to-day existence is similar to that of most Regiments - if you're familiar with any other Arm you'll be at home in the RE.
Whatever else people think of us - and opinions differ wildly - most agree that the social side of the Engineers is superb and if beer and chilli-sauce soaked weekends are your thing, you'll be in heaven.
Will post more when I shake off this damn hang-over