已知公差不为\(0\)的等差数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\)，且\(S_{3}=9\)，\(a_{1}\)，\(a_{2}\)，\(a_{5}\)成等比数列．
\((1)\)求数列\(\{a_{n}\}\)的通项公式；
\((2)\)若数列\(\{b_{n}\}\)满足\(b_{n}=2^{a_{n}+1}\)，求数列\(\{b_{n}-a_{n}\}\)的前\(n\)项和\(T_{n}.\)