The answer is 210.

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say $x$ is the number of soccer balls in each box

$(n + 300)(x) = n^2 +290n -2940$

$(n + 300)(x) = (n^2 +290n -3000) + 510$

$(n + 300)(x) = (n + 300)(n - 10) + 510$

$(n + 300)[x - (n-10)] = 510$

solutions are

$(n + 300) = 510$ and $[x - (n-10)] = 510$

solving for $n$

$(n + 300) = 510$

$n = \boxed{210}$