The \infty -radical madness 2

Algebra Level 5

Let A:=888+888+ A:=\sqrt{8-\sqrt{8-\sqrt{8+\sqrt{8-\sqrt{8-\sqrt{8+\cdots}}}}}} B:=9+99+99+99+99+33333 B:=\sqrt[3]{9+9\sqrt[3]{9+9\sqrt[3]{9+9\sqrt[3]{9+9\sqrt[3]{9+\cdots}}}}} Find BA B-A .

Details and assumptions:

The sign pattern in the first radical is (+) (--+) .

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