Keep 7 away from 9

Discrete Mathematics Level pending

Define \(S\) as the set of all integers of any length such that each integer is made up of distinct digits and contains either a \(7\) or \(9\) in it, but not both (or else, 7 will eat 9 again, like how 7 8 9 (7 ate 9)). Furthermore, let \(T_k\) represent the \(k^{\text{th}}\) term in \(S\) when the integers in \(S\) are arranged from least to greatest (so \(T_1=7\), \(T_2=9\), \(T_3=17\), \(T_4=19\), \(T_5=27\), etc.). Find the sum of the digits of the value \(T_{20014}-T_{2014}\).

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