Question: [![enter image description here](https://i.stack.imgur.com/UBFqR.png)](https://i.stack.imgur.com/UBFqR.png)
The supply voltage is 15 V and RL is 100 kΩ. Find the voltage across each diode and RL.

Is = 0.1 μA, η = 2, and VT = 25 mV.

How can I calculate the net current through RL? I have three unknowns: the net current and the voltages across the diodes.

Answer: 
The voltage across the forward-biased diode is going to be less than 0.7V (the forward voltage with substantial current). If you look at the Shockley diode equation, the current with a large negative voltage (relative to \$\eta\$ Vt) will be essentially -Is. So you can then calculate the forward voltage of the forward biased diode and the voltage across the resistor and verify that the assumptions are correct. Since RL is relatively low resistance, it will be correct. If RL was, say 1G ohm it would not be correct.
You simply solve a system with 3 uknowns.

$$
I = I\_{S}\cdot\left(e^{\frac{V\_{D1}}{\eta V\_{T}}}-1\right),\ 
I = I\_{S}\cdot\left(e^{\frac{V\_{D2}}{\eta V\_{T}}}-1\right),\ 
I = \frac{V\_{s}-V\_{D1}-V\_{D2}}{R\_{L}}
$$

Be careful of the sign of the voltages \$V\_{D1}\$ and \$V\_{D2}\$

Hint: one is <0 the other is >0.