The possibility to predict the epitope recognized by a given T-cell receptor (TCR), based on the Complementarity Determining Region 3 (CDR3) sequence, could significantly facilitate cancer immunotherapy approaches. However, accurate prediction of TCR peptide binding is still a significant challenge. We have developed a new machine-learning-based framework to support adoptive Tcell therapy for cancer. Our framework predicts the probability of the presence of specific amino acids in the epitopes presented by MHC (Major Histocompatibility Complex) that are recognized by a given CDR3 site in a TCR expressed by a T lymphocyte. We also propose a new intuitive approach to the numerical evaluation of the results. Both the conventional and proposed numerical evaluation of our results show that the algorithm captured the data distribution and predicted epitope chains with reliable accuracy. These findings demonstrate that our machine-learning framework lays the foundation for new opportunities in personalized medicine. Moreover, the approach that we propose has a high level of generality and could be used for any kind of sequence-to-sequence problem where specific positions in the predicted sequences are important.