Been screwing around with my brother's 15 for a while now...fairly efficient driver.
The amp used has been a directed 1100d, and we've messed around with a few different boxes, and different wiring configurations (ie different amounts of power to it). Here's what I found - in a 94 nissan sentra (small car).
With ~400 watts, 2.2 cubes @32Hz: Sub was starved for space, low end lacked, but it was a spare box laying around and not meant for the driver. Still pretty loud.
~400 watts, 3.2 cubes @34ish Hz: Sub really shines. This box is about the right volume IMHO, could have a little better low end response, but LOUD, very loud. To my tastes, this was too loud to listen to on a daily basis.
~1100 watts, 2.2 cubes @ 32Hz: Still starved, not a lot of difference.
~1100 watts, 3.2 cubes @ 34ish Hz: LOUD, very very loud. The low end starts to pick up here with the added power. I would never feed the sub more than this much, it just doesn't need it if you're using it for daily use. Driver moves a lot, even in a ported enclosure.
Now, beyond being loud, it is not the most musical sub I've heard. My A series (eD) and my avalanche put it to shame, but for a street beater that I would be OK abusing, it is a great driver.
So, in response to your question, I would assume 1200 would be plenty for an 18. A little more moving mass, but the same motor so I wouldn't think you'd need much more power than the 15 to really get it humming.