[R' E' R2 E2 R', U] // flip two edges
[L E L2 E2 L, U] // flip two edges
[R' D R D' R' D R, U] // orient two corners
[L D L' D' L D L', U'] // orient two corners
// We have a V perm now, which can't be solved with only a commutator because the edge pieces are in an odd permutation (as are the corner pieces). So we do a quarter turn first to fix that.
U
// We start with the edges. (This is a plain 3-cycle. If you know how to solve a U perm, you can solve this in a more straightforward manner.)
M D2 M' U M D2 M' U2 M D2 M' U M D2 M'
// Then the corners. First, we swap the two corners in the front while preserving the rest of the U layer, then do a U2 and undo the front corner swap, then another U2 to finish.
[L U' R D2 R' U L', U2