is it possible to get the Riemann zeros since we know that the number of Riemann zeros on the interval $ (0,E) $ is given by $ N(E)  = \frac{1}{\pi}\operatorname{Arg}\xi(1/2+iE) $
is then possible to get the inverse function $ N(E)^{-1}$ so with this inverse we can evaluate the Riemann zeros $ \rho $ ??
i mean the Riemann zeros are the inverse function of $\arg\xi(1/2+ix) $

No, your formula is wrong.  $N(E)= \frac{1}{\pi} Arg \xi (1/2+iE) $ + a nonzero term coming from the integration along the lines $\Im s =E$ (you are applying an argument prinicple).
Besides, any function $N: \mathbb{R} \rightarrow\mathbb{Z}$ can't be injective for cardinality considerations.
