How can I solve this problem by cvx

The problem is described as

\text{minimize} & t \\
\text{subject to} & \tau+\rhou+uexp{\frac{-x^T*\xi-t-\tau}{u}}-u \leq \lambda \\
& u \geq 0

where \rho, \xi and \lambda are given parameters,x, t, u, \tau are variables to be solved.
Can this problem be solved by CVX?
How to express the constraints in CVX if it could be solved?

Thank you very much!

If the -x^T * zeta term is ignored, the constraint appears to be convex, but only if restricted to u >= 0 (as you have specified)… With the -x^T * zeta term, the convexity or not depends on the values of T and zeta.