Testing deviations from the ΛCDM model using the cosmic microwave background power spectra requires a pristine understanding of instrumental systematics. In this work, we discuss the properties of the observable RℓTE, the correlation coefficient of temperature and E modes. We find that this observable is mostly unaffected by systematics introducing multiplicative biases such as errors in calibration, polarization efficiency, beam and transfer function measurements. We discuss the dependency of this observable on the cosmological model and derive its statistical properties. We then compute the TE correlation coefficients of Planck legacy data and compare them with expectations from the Planck best fit ΛCDM and foreground model.