  Transit timing variations (TTVs) are a powerful tool for characterizing the
properties of transiting exoplanets. However, inferring planet properties from
the observed timing variations is a challenging task, which is usually
addressed by extensive numerical searches. We propose a new, computationally
inexpensive method for inverting TTV signals in a planetary system of two
transiting planets. To the lowest order in planetary masses and eccentricities,
TTVs can be expressed as a linear combination of 3 functions, which we call the
\textit{TTV modes}. These functions depend only on the planets' linear
ephemerides, and can be either constructed analytically, or by performing 3
orbital integrations of the three-body system. Given a TTV signal, the
underlying physical parameters are found by decomposing the data as a sum of
the TTV modes. We demonstrate the use of this method by inferring the mass and
eccentricity of 6 \textit{Kepler} planets that were previously characterized in
other studies. Finally we discuss the implications and future prospects of our
new method.
