You seem to be making good progress. (Why did you miss out the first R line? I don't suppose it will make a huge difference to your regression analysis, but you ought to include it. And P8 is 2703, not 2705.)

Combining equations 8 and 16, and writing Y for (μ/μ*)^{1/2}, which is known, we have

ν_{0} = ν_{e} - 2ν_{e}x_{e}

ν_{0}* = ν_{e}Y - 2ν_{e}x_{e}Y^{2}

so you have 2 simultaneous linear equations for 2 unknowns.