Let $\underline{\vec e}$ be an orthonormal basis in $E^4$ and $W=\{\vec u = \underline{\vec e}X: x_1+2x_2+2x_3=0\}$.
Create a new orthonormal basis $\underline{\vec f}$ so that $W=\{\vec u = \underline{\vec f}Y: y_4=0\}$.
EDIT: I guess you can use $X=TY \implies T=XY^{-1}$ where $X=(1, 2, 2, 0)^t$ and $Y=(0, 0, 0, 1)^t$