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I agree with the posters who say that Cary's advice is juvenile and that it trivializes both the letter writer's marriage and his feelings for his co-worker. Obviously, the writer has to decide what he wants. Taking him at his word, he wants to stay in his marriage. In that case, he can't have sex with his co-worker. Duh.
I don't believe that means he has to give up his feelings for and relationship with his co-worker, which is clearly very important to him. He feels more alive, etc. with her than with anyone (because they're not married, in part). So he needs to be clear with himself that he can't ever sleep with her, that he understands that this is something he wants but can't have. And doesn't really want to have, given the consequences, which is that he is likely to lose both the marriage and the friendship.
What he can do is love her. He can be intimate with her, in every way other than physically. He can show her how much she means to him--without ever saying so, if he thinks that to say "I love you" would be misunderstood.
I have had many such relationships, and they are very important to me. My wife knows and socializes with these women, and knows that I would never have sex with any of them.
Which doesn't mean I can't ever fantasize . . . .