The answer is "yes, but it's complicated."
Film and paper developers are fundamentally the same thing, but they're formulated a bit differently.
The usual Kodak product for developing black-and-white paper is Dektol. It can be used to develop film, but because papers are less sensitive, the mix recommended on the package ends up being a lot stronger than T-Max, D-76 or HC-110 (all developers for film). If you don't want your film developing too quickly, which loses you some control over how it comes out, the developer has to be diluted. The opposite would be true for developing paper with T-Max. Being weaker, you'd either have to wait an awfully long time for the paper to develop or accelerate the process by developing at a much higher temperature or diluting the T-Max less than what the directions on the package specify.
To make either swap (paper in T-Max or film in Dektol) work, you'd have to do some trial-and-error experimentation to figure out what works. This is what Kodak did to come up with recommendations for development times in the documentation for its products.
This kind of experimentation is one of the things that makes chemical photography fun. However, my advice to you as a beginner would be to spend $10 on a bag of Dektol and learn to process paper "by the book" first. This will give you some idea how papers and developers behave under normal circumstances and a benchmark for judging how your experiments are going.