Official solution
\[\overline x = {{2 + 4 + + 10 + 12 + 14 + x + y} \over 7} = 8\]
x + y = 14 ....(i)
\[{(\sigma )^2} = {{\sum {{{({x_i})}^2}} } \over n} - {\left( {{{\sum {{x_i}} } \over n}} \right)^2}\]
\[ \Rightarrow \] \[16 = {{4 + 16 + 100 + 144 + 196 + {x^2} + {y^2}} \over 2} - {8^2}\]
\[ \Rightarrow \] \[16 + 64 = {{460 + {x^2} + {y^2}} \over 7}\]
\[ \Rightarrow \] 560 = 460 + x2 + y2
\[ \Rightarrow \] x2 + y2 = 100 ......(ii)
Clearly by (i) and (ii),
(x + y)2 - 2xy = 100
\[ \Rightarrow \] (14)2 - 2xy = 100
\[ \Rightarrow \] 2xy = 96
\[ \Rightarrow \] xy = 48
Now, |x - y| = \[\sqrt {{{\left( {x + y} \right)}^2} - 4xy} \]
= \[\sqrt {196 - 192} \]
= 2