If I were to use S7 300 PLC would it be ok?

Yes.

Thank you for the support!

You can connect two counters and subtract the value of them sepeately/

Look in the example. The first counter counts 10000, so you can count 10000 x 32000= a lot

Notice: The textblock is not perfect. You can make it perfect with several tekstblock, 

Toeternietoe

You can connect two counters and subtract the value of them sepeately/

Look in the example. The first counter counts 10000, so you can count 10000 x 32000= a lot

Notice: The textblock is not perfect. You can make it perfect with several tekstblock, 

 @Toeternietoe: The original problem that was stated is that the math instruction cannot handle values beyond the Integer boundary. What you suggested is therefor problematic.

My idea was to use a counter to track the difference between IN and OUT pulses. This assumes that the IN is always more than OUT. Also assume there is no need to move beyond the counter's boundary. My idea still does not satisfy the exact requirement.

I was thinking of how one could construct a cascaded counter circuit that would allow both counting up (as you shown) but also counting down. For this idea I have no solution.

The OP is better off using an S7-300 (as he volunteered) if his requirement is set in stone.