If the given quadratic equation has one solution, it follows that its discriminant must be equal to $ 0 $. The discriminant of the given quadratic is given by $ (2b)^2 - 4(a-b) $, and setting this equal to zero, we obtain another quadratic equation $ 4b^2 + 4b - 4a = 0 $. Since the value of $ b $ is unique, it follows that again, the discriminant of this quadratic must be equal to zero. The discriminant is now $ (4)^2 - 4(4)(-4a) = 16 + 64a = 0 $, so it follows that $ a = \boxed{-0.25} $.