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planteamos la diferencia (resta)
x² - (x + 1)² = 103
desarrollo el cuadrado del binomio
x² - (x² + 2x + 1) = 103
saco paréntesis
x² - x² - 2x - 1 = 103
queda:
-2x - 1 = 103
-2x = 103 + 1
x = 104 : (-2)
x = - 52
el consecutivo de -52 es -51
verificación
(-52)² - (-51)² = 103
saludos