The \( \infty \)-radical madness 2

Algebra Level 5

Let \[ A:=\sqrt{8-\sqrt{8-\sqrt{8+\sqrt{8-\sqrt{8-\sqrt{8+\cdots}}}}}} \] \[ B:=\sqrt[3]{9+9\sqrt[3]{9+9\sqrt[3]{9+9\sqrt[3]{9+9\sqrt[3]{9+\cdots}}}}} \] Find \( B-A \).

Details and assumptions:

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

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