Consider the system of equations:
$$\begin{align} 2000 &= \frac{2T}{\chi^2_{2n+2}(1-\alpha)} \\ 2370&= \frac{2T}{\chi^2_{2n}(\alpha)} \\ \end{align}$$
where $\alpha = 0.90$, $n$ is a degrees of freedom, and $T$ is a cumulative time of experience.
How do I calculate $n$ and $T$?
The difficulty is how to replace $\chi^2_{2n+2}(1-\alpha)$ and $\chi^2_{2n}(\alpha)$ for a clear system of equations.
I tried to approximate the chi-square distribution by the standard normal distribution, but I have not found the solution.
How to calculate $n$ and $T$ from this system?