We solved non-equilibrium inverse radiation transfer problem in hydrogen lines, that allows one to carry out the diagnostics of the solar photosphere and chromosphere layers. The Tikhonov stabilizers ensure solution stability to noise and input guesses of the reproduced parameters, suppress false oscillations of the solutions. Using hydrogen lines, we performed test diagnostics of the solar photosphere and chromosphere layers: the maximum absolute error of the temperature recovering does not exceed 70 K. When studying non-LTE hydrogen line formation, we used the quantum-mechanical approach to take into account the linear Stark effect.