Return them anyways and opt for a set of 16's.

But if you MUST keep the 18's, then rubbing would be an issue on a few things. One, is your ride height. Obviously the lower your car is, the more likely you are to rub the tires to your fenderwell. This also makes turning a chore (especially U-turns).

Two, is tire width. Assuming that you have either 205 or 215 wide tires, you're more likely to rub using the 215 tires.

Three is wheel offset. If the wheels you have are between +40mm and +42mm, then you're okay. Anything higher or lower than these numbers, you're screwed.

Finally, your camber. You'd want to have your camber with the proper settings or this might cause your tires to either rub on the inner fenderwell, or the outer fenderwell (which is also why the tire width becomes an issue).

For me, this way too much to worry about, especially for a daily driven car. Not only do you have to worry about rubbing, but you have to be careful where you drive, and how fast. The combination of a big heavy wheel + small sidewall tire + big pothole (bump) + fast speed = no more wheels. Not to mention that you'll end up throwing your suspension out of whack (alignment, camber, caster and toe settings).