  We construct energy-dependent potentials for which the Schroedinger equations
admit solu- tions in terms of exceptional orthogonal polynomials. Our method of
construction is based on certain point transformations, applied to the
equations of exceptional Hermite, Jacobi and Laguerre polynomials. We present
several examples of boundary-value problems with energy-dependent potentials
that admit a discrete spectrum and the corresponding normalizable solutions in
closed form.
