  In non-hermitian systems, the particular position at which two eigenstates
coalesce under a variation of a parameter in the complex plane is called an
exceptional point. A non-perturbative theory is proposed which describes the
evolution of modes in 2D open dielectric systems when permittivity distribution
is modified. We successfully test this theory in a 2D disordered system to
predict the position in the parameter space of the exceptional point between
two Anderson-localized states. We observe that the accuracy of the prediction
depends on the number of localized states accounted for. Such an exceptional
point is experimentally accessible in practically relevant disordered photonic
systems
