I have a 3x8 road bike, but mistakenly bought a 3x10 Shimano derailleur/brake lever. Will it work or should I exchange?
No, the cable pull is different between 8 speed and 10 speed. You will need to exchange it.
There is a detailed explanation here, but the short version is that there are no 8 speed rear derailleurs that are compatible with 10 speed shifters, or vice versa.