MHB How Can You Solve for y in the Equation $(a+b)^{a+b} = a^a + y$?

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$$(a+b)^{a+b}=a^a+y$$ ; sorry i am edited a^b to a^a
Suppose we know a and b.
y in the term of a, b?
 
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How about
$$y=(a+b)^{a+b}-a^b? $$
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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