elliptic k3 surface and Shioda Inose structure

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We know that suppose given two elliptic curves $E$ and $E'$, there is a Kummer surface $km(E,E')$. And I'm curious suppose we know a $K3$ surface is kummer, how do we recover the pair $(E,E')$?

For example, in the note http://www2.iag.uni-hannover.de/~schuett/K3-fam.pdf , in section 10, the authors seem could recover the pair of elliptic curves according to the elliptic fibration. But I have no idea how do they make it. Is there any suggestion for that?

Thanks