You can run any command as a different user using
sudo -u my_user tor-browser-en
If you need to use multiple commands you can do this:
sudo -u my_user sh -c "first && second"
If you want to background the application, you should not do this (it will only work as expected if you're already authenticated with
sudo -u my_user tor-browser-en & # Don't do this
but rather this:
sudo -u my_user sh -c 'tor-browser-en &'
The latter will ensure that you're asked for the
sudo password before the browser is run in the background.