Many proteins remain functionally unannotated. Sequence alignment (SA) uncovers missing annotations by transferring functional knowledge between species' sequence-conserved regions. Because SA is imperfect, network alignment (NA) complements SA by transferring functional knowledge between conserved biological network, rather than just sequence, regions of different species. Existing NA assumes that it is topological similarity (isomorphic-like matching) between network regions that corresponds to the regions' functional relatedness. However, we recently found that functionally unrelated proteins are almost as topologically similar as functionally related proteins. So, we redefined NA as a data-driven framework, TARA, which learns from network and protein functional data what kind of topological relatedness (rather than similarity) between proteins corresponds to the proteins' functional relatedness. TARA used topological information (within each network) but not sequence information (between proteins across networks). Yet, its alignments yielded higher protein functional prediction accuracy than alignments of existing NA methods, even those that used both topological and sequence information. Here, we propose TARA++ that is also data-driven, like TARA and unlike other existing methods, but that uses across-network sequence information on top of within-network topological information, unlike TARA. To deal with the within-and-across-network analysis, we adapt social network embedding to the problem of biological NA. TARA++ outperforms protein functional prediction accuracy of existing methods.