A MATLAB implementation of the Five-Point Algorithm by David Nistér
It now returns all E solutions as well as the corresponding R and t. An example is provided to validate the algorithm.
It appears to already provide proper estimates of the essential matrix. The constraints in terms of rank and singular values are being enforced. At this point the algorithm is returning the first of its multiple solutions. I'm still figuring out how to select the "best" if such exists.