Actually, there is an unknown, simple, & elegant solution that my Talmudic older brother came up with. In fact, it is superior to the classic answer because it works even if both guards are liars.
Here it is (roll the drums):
Which door would you have told me to pick yesterday?
Then pick that door.
If he's a truth teller then its the correct door. If he's a liar then he will lie (today) about the incorrect door he would have told you yesterday, resulting in the correct door!