How to solve the equation and directly determine the value of $\overrightarrow{v}$ in the equation?

$\overrightarrow{v}-a[\overrightarrow{v}\times \hat{y}]=b\overrightarrow{E}$

where, $\overrightarrow{v}$ and $\overrightarrow{E}$ are in the $\hat{x}$ direction, and a and b are scalars.

$\overrightarrow{v}-a[\overrightarrow{v}\times \hat{y}]=b\overrightarrow{E}$

where, $\overrightarrow{v}$ and $\overrightarrow{E}$ are in the $\hat{x}$ direction, and a and b are scalars.