Since the solution of the wave function in vaccum gives two progressive plane waves f(x-ct)+g(x+ct)$f(x-ct)+g(x+ct)$ depending on x$x$ the direction of propagation, in the other side we have the div(Ex)=0$\operatorname{div}(Ex)=0$ so the E$E$ field is static so the wave is not propagating!!!. I can't understand the reasoning here and How this explain that the wave is transverse
