Need fogging alpha equation!

Can't be done isn't in in my vocabulary. :-)

Hm... Maybe I'm going about this the wrong way.

First, I need to know what I want the resulting pixel color to be. And that is governed by this equation:

ResultingPixelR = BackgroundColorR*(1-Alpha) + Alpha*(SpriteColorR*(1-FogAlpha) + FogColorR*FogAlpha)

Sooo...

I have no idea where to go from here. :-)