I have a concrete driveway and bumps are appearing and breaking the concrete. It looks like very bad 'acne' in the concrete. There is a white spongy stuff that I found under one of the bumps and it smells like it might be a tree root. What should I do?

Basically remove tree and the roots. There is no good way to stop this other than cutting some roots that are under the concrete and now the concrete needs replaced. Sorry either way you are going to probably kill the tree or it will come back later after trimming the roots.
To figure any basic root paths of tree roots its at the edge of it canopy.

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This is no easy permanent fix if the tree is still there.