Noise reduction using multiple recordings of the same signal
Is it possible to reconstruct the original pure signal?


No, that is information-theoretical impossible. Also, that signal doesn't exist, probably, to begin with ;)

However, you can definitely increase the the SNR simply by averaging; that becomes pretty obvious when you consider the signal of interest to be correlated within your recording, whereas your noise is claimed to be independent.

If you sum up multiple recordings, the correlated signal's amplitudes will increase linearly with the number of observations, whereas your noises' standard variance only with the square number of that.


  I have two (audio) recordings of one analog signal, I used two separate devices (smart-phones) recording from two different locations.


Find a signal model for your analog signal – it's not just "any signal" (that would be completely indistinguishable from noise), but it's probably very specific. Ask a new question – "I have these and that signal, they follow my signal model (maybe you need help formulating one, another good question), how do find a low-variance estimator for the parameters for that signal model".