\(E=1\cdot1+2\cdot2+3\cdot3+...+15\cdot15\)
\(=1\cdot\left(2-1\right)+2\cdot\left(3-1\right)+3\cdot\left(4-1\right)+...+15\cdot\left(16-1\right)\)
\(=1\cdot2-1+2\cdot3-2+3\cdot4-3+...+15\cdot16-15\)
\(=\left(1\cdot2+2\cdot3+3\cdot4+...+15\cdot16\right)-\left(1+2+3+...+15\right)\)
\(=1360-120=1240\)