Let one number be \(x\). Then the next consecutive number is \((x + 1)\). According to the question: \[ x^2 + (x + 1)^2 = 313 \] \[ x^2 + x^2 + 2x + 1 = 313 \] \[ 2x^2 + 2x + 1 - 313 = 0 \] \[ 2x^2 + 2x - 312 = 0 \] \[ x^2 + x - 156 = 0 \] \[ x^2 + 13x - 12x - 156 = 0 \] \[ x(x + 13) - 12(x + 13) = 0 \] \[ (x + 13)(x - 12) = 0 \] Therefore, either \((x + 13) = 0\) or \((x - 12) = 0\) When \((x + 13) = 0\), then \(x = -13\) [Negative, not acceptable] When \((x - 12) = 0\), then \(x = 12\) ∴ One number is 12 and the other is \(12 + 1 = 13\)