Mhm.
F1= GM1M2 / (2R-x1-x2)^2
Where F1 is the force on object 1, M1 and M2 are the masses of objects 1 and 2, respectively, 2R is their initial separation, and x1 is the distance towards the center that object 1 has travelled from its initial position (and you can guess x2). Now, divide both sides by M1
a1 = GM2 / (2R - x1 - x2)^2
x"1 = GM2 / (2R - x1 - x2)^2
You can make a similar equation for x"2 , and maybe you can get two differential equations you can solve.