# 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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