Distance without the tire in place does not help. How much space is there between the tire and frame at the closest point?
You can use this information to see exactly how much difference there is between your 18" rim and either a ISO 406 or 451 rim
https://www.sheldonbrown.com/rim-sizing.html The only 18" wheel that might be the one you have is the ISO 355 rim "used on Birdy folding bikes". A rough calculation between the 355 and 406 seems to mean the larger diameter tire would be an inch closer to the frame if you used the same brand and model tire.
Somebody asked a similar question about tire size on a recumbent but failed to say that he was using fenders. While the tire would fit if there were no fenders, the closest point was not the frame but the fender.