|x+y|=7.
If x=0, y=+7 or -7 so a single value of x results in two different values for y.
Similarly, if y=0, x=+7 or y=-7 and a single value of y results in two different values for x. Neither x nor y can be the dependent variable, so it’s not a function.
Another way is to write x+y=7, x+y=-7, implying y=7-x and y=-7-x. y is not a function of x.