E35 is a method that solves the last 8 edges of the U and D layers, first 3 D layer edges and then the last 5 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).
Short description: 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.
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 solves columns first, like doing all pairs first and then CMLL (or CMSLL). Really advanced, orient the pairs and then use PEG.