Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.
$$E=2\sqrt{3}-\sqrt{3}+\sqrt{48}$$
Combine $2\sqrt{3}$ and $-\sqrt{3}$ to get $\sqrt{3}$.
$$E=\sqrt{3}+\sqrt{48}$$
Factor $48=4^{2}\times 3$. Rewrite the square root of the product $\sqrt{4^{2}\times 3}$ as the product of square roots $\sqrt{4^{2}}\sqrt{3}$. Take the square root of $4^{2}$.
$$E=\sqrt{3}+4\sqrt{3}$$
Combine $\sqrt{3}$ and $4\sqrt{3}$ to get $5\sqrt{3}$.
