Let the ant weigh x grams and the elephant weigh y grams, and the sum of the two weights is 2a grams, then: x+y=2a.

Multiply both sides by (x-y) to get (x+y)(x-y)=2a(x-y).

That is x2-y2=2ax-2ay.

It can be converted into x2-2ax=y2-2ay.

Add a2 to both sides to get (x-a)2=(y-a)2.

Square both sides to get x-a = y-a.

So x=y