\left\{ \begin{array} { l } { T _ { 1 } = 2 \pi \sqrt { \frac { L _ { 1 } + L } { g } } } \\ { T _ { 2 } = 2 \pi \sqrt { \frac { L _ { 2 } + L } { g } } } \end{array} \right.
Solve for T_1, L_1, L, g, T_2, L_2
T_{1}=2\pi \sqrt{\frac{L+L_{1}}{g}}
L_{1}\in \mathrm{R}
L\in \mathrm{R}
g\in \mathrm{R}
T_{2}=2\pi \sqrt{\frac{L+L_{2}}{g}}
L_{2}\in \mathrm{R}
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