It is experimentally known that the equation of motion for a charge $e$ moving in a static electric field $\mathbf{E}$ is given by:

$\frac{\mathrm{d}}{\mathrm{d}t}(\gamma m\mathbf{v})=e\mathbf{E}$

Is it possible to show this using just Newton's laws of motion for the proper frame of $e$, symmetry arguments, the Lorentz transformations and other additional principles?

$\frac{\mathrm{d}}{\mathrm{d}t}(\gamma m\mathbf{v})=e\mathbf{E}$

Is it possible to show this using just Newton's laws of motion for the proper frame of $e$, symmetry arguments, the Lorentz transformations and other additional principles?