How do I select wider tires for my car while keeping the same overall diameter?

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You would need 285/30 / 18 to match the front., but as well as a rough ride, ( as mentioned), you’re likely to wreck your wheels at any decent sized pothole.

Learn how to do the math using the "aspect ratio" formula.

Diameter is determined by rim size and two times the tire height.   So you got 18 inches plus 2(285 millimeters x 35%).     If you get wider tires you get greater height.   You need to reduce the side wall height by going to 30% or even 25%.   That is going to give you one really hard ride and even the slightest bump could dent your rim.    I would replace all the mismatched stuff with the correct size for the car.  That will solve your rubbing problems.

Do your own algebra. The wheel is 18 inches. We have no clue what car you have  or what the fender clearance is.

the only way to to keep 285mmwide tyres is to reduce the sidewall ..down to 25 ..thats not possible and the ride would be dreadful ..the original tyres were 30mm narrower ..if you went 255.40 its only 3 mm to same diameter as now...and a better ride 

That’s happening because whoever put the 285s on the back also ended up giving making the overall wheel diameter larger.

The 35 is the aspect ratio of the tyre: it’s a sidewall height measurement given as a percentage of tread width. 

So for 285mm wide tread, you have 99.75mm sidewall height (just round it up to 100mm).

For 235mm tread width you get 82.25mm (82mm). 

So your sidewalls are 17.5mm taller than they should be, making the wheel diameter 35mm larger than intended. About 1.4 inches. 

18 inches is 457.2mm. So the wheel diameter with correct tyres is 539.45mm. Multiplying that by pi gives 1694.7mm rolling circumference. 

The wheel diameter with the fatter tyres is 556.95mm, and a rolling circumference of 1749.7mm.

So for every rotation of the driven wheels the car moves forward an additional 55mm, or nearly 2.2 inches. 

It means your speedometer will be reading 3.25% under the true reading and the drivewheel gearing is also effectively 3.25% higher which will have a negative impact upon hill-starts, hill-climbing, acceleration and fuel economy. 

If you want to keep the same tyre width as now then you’ll need ultra-low profile tyres with an aspect ratio of 29% (round that to 30). So 285/30 r18. Those aren’t cheap, they’ll give a harsher ride and you’re more likely to get punctures and rim damage if you hit kerbs and potholes.

If you want narrower tread tyres than 285mm then just go back to stock at 235mm. The 50mm difference is only 2 inches wider. If your desire for wider tyres is purely aesthetic it’s not a big difference as it’s only 1 inch on each side of the tyre. You may also find that grip improves, because going wider increases the contact patch of the tyre and spreads the weight over a larger area. So the rubber doesn’t get forced down onto the hardtop and won’t grip it so well. The difference will be far more noticeable on slippery road surfaces where the narrower standard tyre will definitely give more grip.