This isn't directly supported by the Email Task. I can think of two ways to do this though.
1. Log the output to file too and use the
ReadLinesFromFile task to read the log file and then pass that content into the Body property of the email task. Due to the nature of logging, you won't get 100% of the overall log because the build will still be in process.
2. Write your
own logger which does this all for you.