That sounds like a great piece of beef. Rib eye roast is best when cooked rare to medium, so you sure don't want to overcook it.
A good way to cook it is to smoke it first, let it rest for a little while, then finish it for a short time at high temperature to brown the outside.
With the smoker at 225 degrees, an 18 pound rib eye roast would take 1-1/2 to 2-1/2 hours to reach 125 degrees (depending on the thickness of the roast, its temperature when it went in the smoker, etc). During that time, the beef will gradually come up to temperature. Letting it rest for 15 minutes after that, the temp will equalize throughout the roast, and the temp will continue rising up to around 130 degrees.
Then the rib eye roast would either go on a very hot grill for about 10 minutes (turning to brown all sides), or in a 425 degree oven for 10 to 15 minutes.
After resting again for 10 to 15 minutes, the internal temp will be in the 135-140 degree range, a nice medium rare.
