To give you a pointer: last week I helped a buddy develop a roll of E4 film. The film was quite old (go figure), but the buddy exposed it quite recently. We had no idea of its prior history. We spent two or three evenings mixing the E4 bathes, he even go a bottle of Benzyl Alcohol for this process. To make a long story short: the slides came out completely blank (emulsion extremely soft but was still on there, it contained no image matter, just a slightly milky white layer that came off when you touched it). Three evenings of mixing and processing work went into the trash.
And no, you can not process these old rolls in E6 chemistry, since E2 and E4 films are not properly hardened and their emulsion will float away after FD, especially if you run it at 38°C.
Your E2 roll is likely even older than this E4 roll we processed. If you have a dozen of these rolls or more, use one for experiments and clip tests, and process the rest once you are confident that they still work. If you have only one or two rolls, I'd say get a few nice rolls of recent E6 stock and enjoy the results.