Did Eru have physical form?

[Angry Hill Troll]

Professor Tolkien specifically said that Eru would never take any sort of physical embodiment in Middle Earth, nor would he enter into Ea at all.

It's a bit hard to reconcile this statement with the Athrabeth, where Andreth specifically expresses the belief that at some point in the future Eru would take a physical embodiment in Arda. Granted, perhaps Tolkien has Andreth saying something fanciful which he [Tolkien] knows to be impossible. But in that case, why bother writing the Athrabeth? (Especially since this idea very much follows Tolkien's own religious beliefs).

I assume the quote above is from the Letters, I'm curious when the statement was written, specifically whether it preceeded or followed the Athrabeth (written ca. 1955-1960). Did he back off the idea of Incarnation expressed in the Athrabeth afterwards, or did the Athrabeth contradict his earlier ideas?

In the Notes, CT acknowledges that there were "problems...for the interpretations of my father's thought on these matters"