How is the energy of $x_1\cdot x_2$ related to the energies of $x_1$ and $x_2$?
Knowing the energies of $x_1$ and $x_2$ is not sufficient for determining the energy of $x_3=x_1x_2$. What you can do is determine an upper bound for the energy of $x_3$ given the energies of $x_1$ and $x_2$ and their maximum values:

$$E_3=\sum_{k}\big|x_1[k]x_2[k]\big|^2\le\begin{cases}\max_k\big|x_1[k]\big|^2\sum_k\big|x_2[k]\big|^2=\max_k\big|x_1[k]\big|^2E_2\\\max_k\big|x_2[k]\big|^2\sum_k\big|x_1[k]\big|^2=\max_k\big|x_2[k]\big|^2E_1
\end{cases}\tag{1}$$

From $(1)$ an upper bound for $E_3$ is

$$E_3\le\min\left\{\max_k\big|x_1[k]\big|^2E_2,\max_k\big|x_2[k]\big|^2E_1\right\}\tag{2}$$

Unfortunately, this bound is generally not very tight. For your example you get

$$E_3\le\min\{19.178,17.787\}=17.787$$

but the actual value is $E_3=7.8165$.