integration within system of nonlinear equations

[Lagomorph]

Hi,

I need to solve a system of 2 nonlinear euations. One of the equations contains a definite integral. The integrand and lower limit of this integral contain one of the 2 variables I am trying to solve for. I am trying to use fsolve and quad to get these results, but quad won't accept undefined arguments that I use to get the result
from fsolve.

Can someone help me out with this?

Thanks