Can windows 8 run on core 2 duo e7500 with 4gb ram

Yes it can run windows 8. Because requirement for windows 8 will be same as win7

It will run on that with no issues!

Windows 8 system requirements

If you want to run Windows 7 on your PC, here's what it takes:

1 gigahertz (GHz) or faster 32-bit (x86) or 64-bit (x64) processor

1 gigabyte (GB) RAM (32-bit) or 2 GB RAM (64-bit)

16 GB available hard disk space (32-bit) or 20 GB (64-bit)

DirectX 9 graphics device with WDDM 1.0 or higher driver

I had installed it on a Celeron 331 (Prescott) with 1 Gb DDR and it worked, for sure a Core 2 Duo will work  

A friend has it running nicely on an old C2D E4500 2GB system.

yes this can definitly run on this computer with no problems