A positron is a particle with a mass of zero and a charge of +1. So to solve, you write a balanced equation so that the atomic numbers and total mass are equal on both sides of the equation.
Element X --> F-19 + positron (mass = 0, charge = +1)
F-19 has an atomic number of +9.
Add the +9 to the +1 for the positron means the unknown element has an atomic number of +10 which is Neon.
The isotope of neon would be Ne-19.