Why can a Predictive Parser contain E' -> TE' | ε
... is not valid since we have "left recursion" (a variable that calls itself).


That's not what a left recursion is. That's simply recursion.

Direct left recursion is when a rule $A \to A\alpha$ exists for arbitrary $\alpha$.

Indirect left recursion exists when there's a rule $A \to^* A\alpha$ for arbitrary $\alpha$. Note the star, implying possibly many derivation steps (and if we're being precise, more than one, otherwise it's just direct left recursion).

Only left recursion (whether indirect or direct) is problematic for $\text{LL}(1)$. But your grammar doesn't contain left recursion, only right recursion. Right recursion has the form $A\to^* \alpha A$. See the difference?