The tensor U can indeed be obtained from: U = exp[ En ]
where exp[.] is the matrix exponential.
You can check out the matrix exponential (and other matrix functions) using Matlab (or the free alternative octave).
There are also many good books on these kinds of computations, for example: "Matrix Computations" by Golub and Van Loan.
What I often do to calculate the matrix exponential is to first find the eigenvalues and eigenvectors of En, then take the exponential of the eigenvalues, and then rotate the results back to the original coordinate system.
Jorgen Bergstrom, Ph.D.