Maybe YOU need to set some different rules regarding the email situation? Maybe you're right, it isn't so healthy to be getting them, because it seems that however T answers them, there is something triggering or disappointing in it for you.
The thing is, yes, it isn't a friend emailing you, it's T......and for her, it is work. It may be a loving work and a loving work relationship, but it is still work. And I know that is disappointing to you, to think of love equating to work in this case.......maybe some parts of you need to work more on accepting the reality of the T relationship, that love does exist within the framework, but it's still limited to existing within certain necessary boundaries....
I don't have anything so wise either, because I struggle with the limitations of my T relationship sometimes too.....I mean, I am not wanting her to be my friend, but I wish the word love and the feeling love could be freely expressed is all! So I think that your T is open to the discussion and to helping you accept your love for her is a wonderful thing.....