A set of numbers Problem: Let $E(x)$ be the number defined by the following expression
\begin{equation*}
 E(x)=\sqrt[3]\frac{x^3-3x+(x^2-1)\sqrt{x^2-4}}{2}+\sqrt[3]\frac{x^3-3x-(x^2-1)\sqrt{x^2-4}}{2} 
\end{equation*}
where  $x$ is a real number and 
$\sqrt[3]{Z}$ denotes the real cubic root of the real number $Z$.
Determine the set
$ \{E(n); n\in \mathbb{N}$ and $n > 1\}$ 

$$E(x)^3=(Y+Z)^3=Y^3+3YZE(x)+Z^3\\
=x^3-3x+3E(x)\sqrt[3]{\frac{x^6-6x^4+9x^2-x^6+6x^4-9x^2+4}4}$$
