First up I have to openly state I checked his texts. He closes things down quickly on the computer if he hears me coming which always makes me wonder so I checked on Friday. We have a chequered history for this. He has read my emails and messages in the past and got very angry if he thought i had communicated with men. Even long standing friends came under his suspicion. Anyway, there is an email exchange on the shared computer. Nothing I would ever have been overly bothered about if I didn't have this massive resentment for the years of invading my privacy and accusing me of cheating (when i absolutely have not, not in word nor deed). So I don't know if it's my anger making more out of it or if something is amiss. It's clearly someone he knows from the past (not sure how but not met up for many years) and they're arranging to meet for coffee. These emails start from a point where it's obvious previous conversations have taken place but been deleted or conducted by some other medium not text. She is quite flirty and ends with kisses (that's not a bother, some people do) and he is relatively matter of fact. So far so mundane. BUT he has kept this a secret and last night after we'd been away for the weekend he replied to her text from the previous day at 4am. All texts are deleted off his phone (I checked this evening), but he's not that tech savvy so don't think he realises they are on the computer. I am really pissed off that after the stuff he put me through with his constant snooping and allegations he would do this. Is there a chance this is innocent? Ps partner not husband but live together.
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You don't need the pretext of his infidelity to end it if you want to. The situation sounds difficult, but not impossible, to get out of, but it also sounds utterly draining. 
I don't know if he's definitely cheating but he's absolutely a hypocrite if he goes off at you for talking to men when he's been hiding email correspondence with a woman for months! And as someone else said, cheaters do sometimes accuse their partner of cheating or become excessively paranoid as a reflection of what they're doing themselves.
Either way, and given the added context of your second post, you sound desperately unhappy 
I know it can be difficult to disentangle two lives when they have become enmeshed but you truly don't need any evidence of cheating, or anything at all, if you want to leave him. You can just do it.
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