Solve R_{L}T_{L}=R_{S}T_{S}quadR_{L}=40R_{S}=80T_{S}=T_{L}-5

$$R _ { L } T _ { L } = R _ { S } T _ { S } \quad R _ { L } = 40 R _ { S } = 80 T _ { S } = T _ { L } - 5$$

Evaluate (complex solution)

$$R_{L}T_{L}=R_{L}R_{S}T_{S}\text{ and }R_{L}R_{S}T_{S}=40R_{S}\text{ and }40R_{S}=80T_{S}\text{ and }80T_{S}=T_{L}-5$$

Solve for T_S

$$\left\{\begin{matrix}T_{S}=-\frac{\sqrt{1610}}{2}+20\text{, }&R_{L}=-8\sqrt{1610}-320\text{ and }T_{L}=1605-40\sqrt{1610}\text{ and }R_{S}=40-\sqrt{1610}\\T_{S}=\frac{\sqrt{1610}}{2}+20\text{, }&R_{L}=8\sqrt{1610}-320\text{ and }T_{L}=40\sqrt{1610}+1605\text{ and }R_{S}=\sqrt{1610}+40\\T_{S}=0\text{, }&R_{S}=0\text{ and }R_{L}=0\text{ and }T_{L}=5\end{matrix}\right.$$

Solve for T_L

$$\left\{\begin{matrix}T_{L}=1605-40\sqrt{1610}\text{, }&R_{L}=-8\sqrt{1610}-320\text{ and }R_{S}=40-\sqrt{1610}\text{ and }T_{S}=-\frac{\sqrt{1610}}{2}+20\\T_{L}=40\sqrt{1610}+1605\text{, }&R_{L}=8\sqrt{1610}-320\text{ and }R_{S}=\sqrt{1610}+40\text{ and }T_{S}=\frac{\sqrt{1610}}{2}+20\\T_{L}=5\text{, }&R_{S}=0\text{ and }R_{L}=0\text{ and }T_{S}=0\end{matrix}\right.$$