Because one sound hidden from your hearing by another is not the "recording", nothing can be done about it. You will not succeed with "noise canceling" perhaps with another microphone to pick up just the "noise", it cannot work well although you might get some improvement of pure tones, perhaps the whine. You may be able to EQ some of the noise away, assuming the whole record chain is linear, and perhaps cancel a bit more, and this is where a very wide recording dynamic range can be helpful. To get full cancellation you need several things, each of which is largely unachievable. These are exact level matching to a tiny fraction of the level difference (say to -50 dB), exact delay matching over the frequency range, and exactly the same frequency response, again to huge accuracy. Try some experiments with white noise fed to two channels, one inverted, on a mixer. Tiny changes in gain, eq etc lead to little cancellation, which should be perfect. Add 2 microphones in different positions to the picture and you are lost!