Eliot said similar things in his essay of Yeats and, I assume, elsewhere. I don't see that this is very close to the one you sent first except in its general idea--not the words. It was an idea not just in this point about Shakespeare.

>>> Rickard Parker <[log in to unmask]> 07/19/12 6:14 PM >>>
In my original message I sent a paragraph that appeared to create
an Eliot quotation. It was:

Josephine agreed with T S Eliot that we understand the poet’s
work better if we understand something of the poet’s life. As
Eliot said: "The poet always writes out of his personal life;
in his finest work out of its tragedy, whatever it may be,
remorse, lost love or loneliness."

There is this real quotation however:

Shakespeare, too, was occupied with the struggle--which

alone constitutes life for the poet--to transmute his personal

and private agonies into something rich and strange, something
universal and impersonal. The rage of Dante against Florence,
or Pistoia, or what not, the deep surge of Shakespeare's general
cynicism and disillusionment, are merely gigantic attempts to
metamorpose private failures and disappointments. The great poet,
in writing himself, writes his time.

T.S. Eliot, Selected Essays 1917-1932

Shakespeare and the Stoicism of Seneca

p. 117

Rick Parker