The E(X)e Jahn-Teller system is studied in the strong coupling limit on a cluster model using the transformation and energy minimization method developed originally for orbital triplets by Dunn and Bates (1989). Simple analytical expressions for the ground and first excited states together with their energies are derived when the potential energy surface is warped by either anharmonicity or quadratic coupling. Anisotropic corrections are then added to both the vibronic states and their energies and the inversion splitting is calculated. It is shown that the results obtained are in agreement with previously published numerical results.