arcgis 10.0 - How to Select "Inverse" of intersection of two polygon layers?

I'm wondering if there's a way to intersect two polygon layers, take the intersection, and remove that from one of the polygon layers, making a new layer out of whatever is left over? Basically, the idea I have is one of "punching holes" in a map of Africa where the holes are points around which I construct some sort of buffer. I have QGIS and ArcGIS 10.0. Is there a built-in or user created script for this?