The only real way is to grow your side hair out as much as you can and get a hairpiece with a density which is not too much denser what you have been able to grow out. With the undercut styles that are currently popular you don't need a lot of density on the sides, but obviously if you put a thick mop of hair on top which no one could possibly have grown in the time available, it will be a giveaway.

The longer (in time) you can grow your side hair out, the higher density of unit you will be able to get. If you can wear a hat to work obviously it's much easier. If not, then you need to take as much vacation time as you can. I guess 3 weeks of vacation plus some scalp make-up is enough to allow you to match it with a lightish density unit (maybe 90% but YMMV). You can always increase gradually to a higher density once people are used to your new look.

One thing which is often said here, but which is nonetheless true, is that 99% of people have no interest in other people's appearance, and will only notice a change in your appearance if it is really extreme. It's a good idea to create a distraction, like wearing glasses or growing a beard or a moustache, to divert attention from what's going on on the top of your head.