You will also be able to get an assumed position by reducing the sight. Starting from your sight, adjusted for dip, sextant error and so on you then compare it to the altitude you calculate the sun would be at if you are where you thought you were. The difference between the observed and calculated altitude is your intercept.
you end up with a single line of position (it’s actually a small circle you could be anywhere on but for practical purposes in this case can be a straight line) and you can also calculate the azimuth of the sun. The azimuth is perpendicular to your line of position and the difference between calculated and true sextant angles gives you how far down that azimuth from where you think you are your line of position crosses it. Where this azimuth crosses the line of position is your intercept terminal point and gives you a reasonable idea of where you might be. You could then just use either a plane or Mercator calculation to get the distance between your and your oppo’s position.
No experience doing celestial in aircraft though, all mine was at sea at rather more gentlemanly pace with a calculator and plenty of time to work the tables. The FAA navigator’s handbook is freely available online, and I guess most of us have plenty of time on our hands right now!