ISL 1979 Problem 21

Let $E$ be the set of all bijective mappings from $\mathbb R$ to $\mathbb R$ satisfying $$f(t) + f^{-1}(t) = 2t, \forall t \in \mathbb R,$$ where $f^{-1}$ is the mapping inverse to $f$ . Find all elements of $E$ that are monotonic mappings.