The constructible universe $L$ is too thin for large cardinals greater than measurable. To build $L$-like inner models for large cardinal, it is natural to think about "adding" the evidences into the model. For example, $L[U]$ is an inner model for measurable cardinal. However, the situation becomes much more complicated beyond measurable. One reason is that $L[U]$ can contain only one measurable cardinal not two, which I knew. And I was told somewhere that

if $\kappa$ is a some strong cardinal witnessed by an/some elementary embedding(s) $j$, and $E$ is an extender generated from $j$, Then $L[E]=L[U]$ where $U=E_{\{\kappa\}}$.

Is the statement true? If true, how to prove it? If not, how to argue that it is necessary to develop much more complicated technique to build inner model for larger cardinals?