There are uncountably many sentences of countably infinite length. The sentence at hand is countably long and thus cannot contain them all. It cannot even contain two countably infinite strings that don't have a common infinite suffix.
I think the question needs to be cleaned up a bit. In particular, the "uniquely and completely describes every English statement possible" part is iffy. First, this statement is infinite and English statements are finite. Second, this statement specifies that there is the letter "T" at the beginning which is obviously not true for all statements.
Do you want to say that every English statement can be converted to this form?
This is the (late) weekly open thread. See the tag. You'd think we could automate this. The traditional boilerplate follows.
If it's worth saying, but not worth its own post, then it goes here.
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