How to Extract Parameters from Non-Invertible Functions Using Experimental Data?

[Sebastian]

Homework Statement

This is for a project in String Theory, but it's actually a curve fitting question. I've derived the two equations given below, for the energy $E$ and angular momentum $J$ of a meson as a function of some quantities $\omega, T, x$. Now, I have experimental data for $E$ as a function of $J$ for each meson (for example, for the rho meson E(1) = 775.5 MeV, E(2) = 1318.3 MeV, etc.). I need to use the data in order to extract $\omega, T, x$ for each meson. Since the functions I found are not invertible, I don't know how to continue from here. Any help would be appreciated :)

Homework Equations

$E = \frac{2T}{\omega}\left(\arcsin x + \frac{1}{x}\sqrt{1-x^2}\right)$
$J = \frac{T}{\omega^2}\left(\arcsin x + x \sqrt{1-x^2}\right)$

The Attempt at a Solution

See above.

 

[Sebastian]

Anyone..?