Where are you measuring? A 7.5" wheel is actually 8.5" wide if you're going from 'rim' to 'rim.'

Wheels
 

I am measuring the wheel width from lip to lip

Measure the inside of the lip not the outside. There is about 1/2" discrepancy. Round down. Not really possible with tire mounted. Its probably either a 7.5 or 8" wide wheel if your measuring total width from outside. Still need to figure out offset - in MM would be helpful. I don't know how back spacing measurements correlate myself, but someone else might.

Wheels
 

I am going to take the wheel to the tire shop and have them measure the width with their tool
as for the offset it is measured from the inside lip to the mounting face which i measure to be 158mm

wheels
 

ok now I have the wheels measured and they are 7.5 and not 8.5 inches.
I will look for a replacement wheel that is 9 inches in order to fit 255/35/18 tires

offset
 

Now this offset business is getting complicated. In my previous post I indicated that I had a negative 158mm offset.
This is obviously not correct. So I have a 7.5 inch wheel and in order to find the offset I measure from the face of the backing plate (mounting surface) to the centre of the wheel.
It looks like I will need to purchase new wheels in order to mount 255/35/18 tires on the rear. The bolt pattern I believe is 5x122mm. Can someone who has used this combination
please give me the correct offset that I need in order to make this work. I don't want to have to roll the fenders.

Dude WHAT.

All of your math is way off.

If the wheels were previously on your S2000 they are 5x114.3

Your offset is absolutely not -158. It is most likely around 40.

I would throw those wheels on craigslist.

Go buy wheels that are the right size for our cars. 7.5 all around is a bad choice. 17" will ride more nicely & look less skateboardy (some S2000 pull it off, not many).

Offset
 

Ok I understand that I can't mix the wheel size between the front and the rear. I am looking at replacing my 18 inch wheels with 17's. I need to know if this combination will work. 225/45/17 up front and 255/40/17 on the rear.
I don't want to roll my fenders. If this works, assuming I use 8 inch wheels up front and 9 inch on the rear what offset do I need? I am looking for something black that would be similar to the picture below.

https://cimg6.ibsrv.net/gimg/www.s2k...2ba86427f8.jpg

Look up Enkei PF01 if you don't want to roll your fenders. Pretty sure they come in black.

17/8 +50F

17/9 +60R

Lol -158mm offset. No no. Thats no where near right.

Everything I see about those wheels is like 10+ years old. Their website doesn't work and from some very old looking images I would guess the wheels as 18x7.5 +45. You are on the right track getting rid of them and putting on some wheels closer to OEM AP2 spec like Junky posted. The PF01 are a great choice. TSW has a few options with similar high offsets as well.