what type of corolla do you have, cause unless its a new sportivo or a very worked 4age, the type R will still woop you to start off with, ten bucks says the type R has much better front tyres for a start and suspension.
Look into better shocks springs etc, these help keep the wheel in contact with the road, and stiffer springs will help to stop the weight transfer, after that if whiteline make an anti lift kit try that. Personally though why are you racing a type R