If your transmittance measurement procedure is correct negative value of Reflection should not be meaningless. What is your material? Is it free standing or what is your substrate? Have you done baseline correction properly? Did you consider optical losses in R=1-(A+T) ?
If this ( A+T>1 ) was correct, your sample would "produce" energy - more light is transmitted and absorbed than incident. I would consider this to be highly unlikely and rather double-check the setup. It would be interesting to know how you do the measurement, especially for A.