Hint: $$\begin{align*} T(n) &= 2T(n-1) + n \\ &= 2^2 T(n-2) + (2n + n) - 2 \\ &= 2^3 T(n-3) + (2^2n + 2n + n) - (2^2 \cdot 2 - 2) \\ &= 2^4 T(n-4) + (2^3n + 2^2n + 2n + n) - (2^3 \cdot 3 + 2^2 \cdot 2 + 2^1 \cdot 1) \\ &= \dots \end{align*}$$$$\begin{align*} T(n) &= 2T(n-1) + n \\ &= 2^2 T(n-2) + (2n + n) - 2 \\ &= 2^3 T(n-3) + (2^2n + 2n + n) - (2^2 \cdot 2 - 2) \\ &= 2^4 T(n-4) + (2^3n + 2^2n + 2n + n) - (2^3 \cdot 3 + 2^2 \cdot 2 + 2^1 \cdot 1) \\ &= \cdots \end{align*}$$
If you are familiar with the required methods, you can also solve it using generating functions (and, e.g., techniques from here or chapter 7 of "Concrete Mathematics" by Graham, Knuth, et al.).