How to change white color to black color and black color to white color displaying from the monitor?
Any developed software? Should I write a program with APIs? (and... with which APIs?)
I'm assuming that you actually want to invert all colors, not just black and white. In Windows 7, (and probably Vista and Windows 8 too) start magnifier (Start menu → Accessories → Ease of Access, or ⊞ Win+U), click the gear icon to show settings, and check "turn on color inversion".
This only works if you're using Aero, not with the classic theme, or if your graphics driver doesn't support Aero.