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Suppose $S_n=\sum_{i=1}^{n}\sqrt{a_n}$，and $a_{n+1}+S_n=1+(S_n)^2$，How to solve $a_n$?

I know $a_{n+1}$ could be replaced with $(S_{n+1}-S_n)^2$, so that

$S_{n+1}^2 -2S_{n+1}S_n+S_n-1=0$

but I still wondering how to solve this equation?

user61028
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