Is it possible to use the load line analysis technique on two diodes?

I understand the load line analysis is a way of solving two equations. In the two diodes case, I also have two equations.

In number 5 for example, I will try to get \$V_{D1}\$ using the load line method.

1. \$5 = - V_{D1} - V_{D2}\$

   \$ I_{d2} = I_{s2} \times ( \exp( V_{D2} / (2V_T) ) - 1) \$

   \$ V_{D2} = 2 V_T \times \ln(I_{d2} / I_{s2} + 1)\$

   \$ I_{d1} = I_{d2}\$ because the diodes are in series

So Equation 1 is \$5 = -V_{D1} - 2 V_T \times \ln (I_{d1} / I_{s2} + 1)\$

2. Equation 2 is \$I_{d1} = I_{s1} \times ( \exp(V_{D1} / (2 V_T)) - 1)\$

So now I have two equations in \$V_{D1}\$ and \$I_{d1}\$, but my calculator cannot solve them.