1. Analyze Amplitude: The standard wave equation is $E = E_0 \cos(\omega t \pm kx)$. Comparing with the given equation, the amplitude $E_0 = 10 \text{ V/m}$. Thus, statement (3) is correct.
2. Analyze Direction: The argument of the cosine function is $(10^7 t + kx)$. The positive sign between the time and position terms ($+$) indicates that the wave is propagating in the negative $x$-direction . Thus, statement (4) is incorrect.
3. Analyze Wavelength: The angular frequency is $\omega = 10^7 \text{ rad/s}$. The speed of light in vacuum is $c = 3 \times 10^8 \text{ m/s}$. The wavelength $\lambda$ is given by $\lambda = \frac{2\pi c}{\omega}$. $\lambda = \frac{2\pi \times 3 \times 10^8}{10^7} = 60\pi \approx 60 \times 3.1416 = 188.5 \text{ m}$ Thus, statement (1) is correct (188.4 m is a reasonable approximation).
4. Analyze Wave Number: The wave number $k = \frac{\omega}{c} = \frac{10^7}{3 \times 10^8} = \frac{1}{30} \approx 0.033 \text{ rad/m}$. Statement (2) claims it is $0.33 \text{ rad/m}$, which is incorrect by a factor of 10.

Therefore, only statements (1) and (3) are correct.