The theory behind it is simple: Subtract each audio sample in B from each audiosample in A.

You can do the same thing in your DAW¹ by putting A (e.g. the original) onto one channel and B (the processed sound) onto another. Then you invert the phase of B and listen to/export the sum.

This trick works also for audio gear that claims it does amazing things to your sound (here you just need to make sure to match the levels if they have been changed). Then you can look how much of the signal has truly been affected by your 1000 bucks silver speaker cable.

¹ Digital Audio Workstation, something as simple as Audacity should do the trick