TH-TMO 2018 Problem 10

Let $a,b,c$ be non-zero real numbers.Prove that if function $f,g:\mathbb{R}\to\mathbb{R}$ satisfy $af(x+y)+bf(x-y)=cf(x)+g(y)$ for all real number $x,y$ that $y>2018$ then there exists a function $h:\mathbb{R}\to\mathbb{R}$ such that $f(x+y)+f(x-y)=2f(x)+h(y)$ for all real number $x,y$ .