Fit data with coupled equation

Hi there, I have some measured data as a function of say the temperature=E(T). I want to fit this with some expression of the form: E( T ) =a + b T ^2 + x( T )* T

where I first have to numerically solve for x(T)

x exp(x) =((c/T)- x )*exp(d/T)

I'm finally interested in the parameter c and d, they include the physical meaning of the experiment, but I have so far not really an idea how to start with fitting my data E(T) with such a coupled equation. If you could give me some hints where to look I would greatly appreciate it! Thanks in advance!

[Julian]

No one any idea? Looping through it and fit each parameter independent would be very tidious

[Roger Wohlwend]

It seems to me that there is no unique solution for x. How can I solve for x when the parameters c and d are not defined?