TTU product support for "forward" Teradata Database releases varies by TTU product, so you need to consult the release notes for each TTU 13.10 product that you are interested in using with Teradata Database 14.10.
Some, but not all, TTU products support "one forward" Teradata Database release -- that combination would be a TTU 14.0 product working with Teradata Database 14.10. Keep in mind, however, that none of the newer database features are supported in conjunction with an older TTU release.
The Teradata JDBC Driver has a support policy of supporting "four forward" Teradata Database releases, which is more than other TTU products. But the same caveat is in place -- none of the newer database features are supported in conjunction with an older version of the Teradata JDBC Driver.