There are infinitely many possible answers.
For any coprime q, the pair 16/q and q/2 will do. So, for example,
q = 3 gives 51/3 and 11/2,
q = 5 gives 31/5 and 21/2,
q = 11 gives 15/11 and 51/2.
2 and 53
1 2
143 and 2
4400 and 2
The question is misguided because, in fact, two mixed numbers can be added to equal 2. For example: 31/2 and (-11/2), when added together, give 2. There is no reason to restrict mixed numbers to positive mixed numbers!
The numbers are -10 and -70
1 and 83
1 and 2
1215 and 2
198*2
43 and 2
16 and 17