  A ring is said to satisfy the $2$-nil-sum property if every non central-unit
is the sum of two nilpotents. We prove that a ring satisfies the $2$-nil-sum
property iff it is either a simple ring with the $2$-nil-sum property or a
commutative local ring with nil Jacobson radical, and we provide an example of
a simple ring with the $2$-nil-sum property that is not commutative. Moreover,
a simple right Goldie ring has the $2$-nil-sum property iff it is a field.
