That's really a tire rather than a rim size. (The second number in a rim size is usually the internal width in mm and the CR18 isn't =that= wide.)
Rim/tire sizing makes very little sense. For the full story, check out Sheldon Brown's article.
http://sheldonbrown.com/tire_sizing.html
What I find especially odd is that the 'C' is so often put after the width in millimeters. The wheel size designation is '700C' (which is not, in any practical sense, a real measurement of anything). Following the width in millimeters with half the tire size designation is confounding for new riders. I understand =why= it's done, I just don't think it's a good idea.
It would be so nice if we could just dump the meaningless and obsolete designations in favor of bead seat diameters and metric widths. Of course, if we eliminated the confusion then everybody would be able to order their own tires with confidence instead of throwing up their hands in disgust and paying the LBS premium to figure it out.
In any case, I always refer to tires either by BSD and width or, if necessary, by the French size and metric width. So I would call your tire 700C x 35mm or 622 x 35. According to Sun the rim is specified as 622mm BSD, 612mm ERD , 22.5mm width and 15.5mm depth.
Confused yet?