E35 is a method that solves the last eight edges of the U and D layers, first three D layer edges and then the last five ones always preserving all corners and E-slice edges. In most cases the first part also solves the centres.
E35 is not a compleate brute force method, it uses a combination of intuition and algorithms, an advanced user even include ELL in the method to save turns in some cases but most times you end in EPLL or 5 edge permutation. It is much as Roux last step but here orientation is done after all centres are solved to make recognition easier/faster so the M-permut used last in Roux is not really useful here (you solve centres and BD before orient instead of RU/LU after).
- E3 part First pair up RD and LD edges, then place them together with R and L centres or simply do one at the time, the first one as a pair with the centre and the second using AUF M' U/U'/U2 M, last palce BD + B centre as a pair.
- E5 part Next use Roux M' U M style to orient last 5 edges (9 cases, newer the worst 6 edge case of Roux). If possible also place FD during orientation and end in EPLL. Else use AUF M' U2 M to place it and then do EPLL or use 5-edge permutations.
E35 may be used in CF if the E-slice is solved after the corners or in any method that solves columns first, like doing all pairs first and then CMLL (or CMSLL). If you want to go really advanced you orient the pairs and then use PEG. The E5 part is a stand alone method that can be used for Roux if the BD edge and centres are solved before edge permutation.