Diode Circuits using expotential model
Writing down KCL equations in \$v_{OUT}\$, while assuming all diodes are equal such that \$v_D = \frac{v_{OUT}}{3}\$ (current flowing in = current flowing out):

\$\frac{10V-v_{OUT}}{R_1} = \frac{v_{OUT}}{R_2} + I_s\left(e^{\frac{v_{OUT}}{3n\ U_t}}-1\right)\$

This is a transcendental equation that cannot be solved analytically. It should be solved using a numerical method, which is what circuit simulators do.