How to get eigenvalue equation with Transfer Matrix Method?

I’m studying a paper on physics entitled "Bound State of the One-Dimensional Dirac Equation for Scalar and Vector Double Square Well Potential"

It states in the paper that "It is necessary to solve the transcendental complex equation given by equation (28) in order to obtain eigenvalues ($E=E_n$) of a bounded particle"

Equation 28 is obtained from calculations using the transfer matrix method, where

But, I have a hard time understanding the particular steps in math involved. I can’t understand how to obtain eigenvalues ($E=E_n$) of a bounded particle from the equation (28).

Does anyone understand about transfer matrix method? please help me if anyone knows. It would be helpful if someone could give me a hint of what was going on.

Thank you.