I think the Student Manual more or less stands as its own text. Obviously, there are some complements to TAOE, but I don't think it's necessary for the manual. TAOE is more like a cookbook than a textbook; it makes for a great reference but I wouldn't recommend trying to learn directly from it.
If you're curious, I have some scans that you can use to preview the book.
If you're curious, I have some scans that you can use to preview the book.