$E_{6(n)}$ means that $n$ is the dimension of the group $E_6$ minus twice the dimension of a maximal compact subgroup.

<A HREF="https://ncatlab.org/nlab/show/maximal+compact+subgroup#ExamplesForLieGroups">example</A>: $E_{6(6)}$ of dimension 78 has maximal compact subgroup ${\rm Sp}(4)/\mathbb{Z}_2$ of dimension 36.