$E(x) \equiv 17x + 4 \pmod{26}$ $E(x) \equiv 17x + 4 \pmod{26}$
the numbers 4,7 and 15 need deciphered 
My answer spells ART correct me if wrong.

Correct, $\,17x\!+\!4\,$ has inverse $\,17^{-1}(x\!-\!4)\equiv 12\!-\!3x\ $ by $\ \dfrac{1}{17}\equiv \dfrac{1}{-9}\equiv\dfrac{3}{-27}\equiv \dfrac{3}{-1}$
Therefore $\ 12\!-\!3x\ $ decodes $\, 4,7,15\, \mapsto\, 0,17,19\,\mapsto\, $ A,R,T in English
