In Exile you have to walk between the pillars in a certain route until you hear a click which signifies the door opening. If you step on a wrong tile you get teleported back to the start of the room and have to do it again! I recommend saving after EVERY move until you reach the door.
I don't remember the exact route but you have to start off heading left until you're near the wall (but not at it) and then go sort of up and right. But, like I said, save after every move so if you get teleported you don't have to start the room again.