Relatable Integers

We know that \[ 89 = 8 + 9^2. \] Including 89 shown above, how many 2-digit integer(s) satisfy the equation \[ \overline{ab} = a + b^2 ? \]

Clarification:
For example, if \(a=7\) and \(b=4,\) then \(\overline{ab} = 74.\)

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