One Source Signal Separation
Let's sum your problem. Assuming the transfer function of the whole signal transmission chain from the source 1 to the recorded signal (DAC, speaker, room, microphone, ADC...) is $h_1$ (and $h_2$ from source 2 to microphone), then the signals you have complete access too are:


$(h_1 \star x_1)(n) + (h_2 \star x_2)(n)$ (the resulting signal)
$x_1(n)$ (one of the original signals).


And your problem is that you want to recover $x_2$? Then this is the same setup as this question, and certainly not a problem of source separation - since one of the signals is already known (up to a convolution). You can get an estimate of $h_1$, and recover $h_2 \star x_2$. And if you can assume that $h_1$ and $h_2$ are similar, you can try inverting $h_2$ and get a result closer to $x_2$.

It would be a true BSS problem is you had no prior information about both $x_1$ and $x_2$, in which case it would have been intractable (unless some assumptions can be made about the way these sounds are produced - eg one of them is speech and the other is background music).