How to extract unknown packet from collision between said packet and another, known packet?
As JRE said, deconvolution is not what you need.  You need to subtract the known signal from the combined signal to leave the unknown signal by itself.

If the signals are baseband signals (I'm aware that yours are modulated- I will get to that later in the answer) then you need to know when the known signal started and how strong it is.  You can get an estimate of both of those things through cross-correlation.  You cross-correlate the combined signal with a clean reconstruction of the known signal.  You should get a strong peak at the location of the known signal.  From this you can determine when the signal started.  You can also estimate the signal amplitude using the peak's amplitude.

$$
y[n] = \sum\limits_m x[m]r[n+m]
$$

This is the definition of cross-correlation, where x[n] is the combined signal, r[n] is the reconstructed known signal, and y[n] is the cross-correlation.

$$
y[n] = \sum\limits_m (s_1[m] + s_2[m] + noise[n])r[n+m] \approx \sum\limits_m s_2[m]r[m]
$$

In this equation I have broken x[n] into its constituent parts: $s_1[n]$ (the unknown signal, $s_2[n]$ (the known signal), and noise.  If we assume that $s_1[n]$ does not correlate strongly with $s_2[m]$ then we can simply disregard $s_1[n]$ and the noise term with the understanding that they will both likely add some error to the result.

So, the peak's amplitude is approximately equal to $\sum\limits_m s_2[m]r[n+m]$.  Since you know $r[n]$ completely, you can use this value to determine the amplitude of $s_2[n]$.

Once you know the start time and amplitude of $s_2[n]$, you can subtract it out of $x[n]$, leaving only $s_1[n]$, the noise term, and whatever error was in your estimate of $s_2[n]$.

If the packets are modulated the same basic process is followed, except you will also have to find/determine any carrier offset in $s_2[n]$, and it's phase.  The phase you can get from the cross-correlation peak's phase.  The carrier offset you can find using the fourth power technique (for PSK signals), or by searching for the best cross-correlation result at various carrier offsets.