  Event shape observables have been widely used for precision QCD studies at
various lepton and hadron colliders. We present the most accurate calculation
of the transverse-energy-energy correlation event shape variable in
deep-inelastic scattering. In the framework of soft-collinear effective theory
the cross section is factorized as the convolution of the hard function, beam
function, jet function and soft function in the back-to-back limit. A close
connection to TMD factorization is established, as the beam function when
combined with part of the soft function is identical to the conventional TMD
parton distribution function, and the jet function is the second moment of the
TMD fragmentation function matching coefficient. We validate our framework by
comparing the obtained LO and NLO leading singular distributions to the full
QCD calculations in the back-to-back limit. We report the resummed
transverse-energy-energy correlation distributions up to N$^3$LL accuracy
matched with the NLO cross section for the production of a lepton and two jets.
Our work provides a new way to precisely study TMD physics at the future
Electron-Ion Collider.
