$\begin{array}{l} \sqrt {x + 2010} = t\\ \Rightarrow x + 2010 = t\\ \Rightarrow x = t - 2010 \Rightarrow {x^2} = {\left( {t - 2010} \right)^2}\\ PT \Rightarrow {\left( {t - 2010} \right)^2} + t = 2010\\ \Leftrightarrow {t^2} - 4019t + 4038090 = 0\\ \Leftrightarrow \left( {t - 2010} \right)\left( {t - 2009} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l} t = 2010\\ t = 2009 \end{array} \right.(TM) \Rightarrow S = \left\{ {2009;2010} \right\} \end{array}$