The relation between linewidth and energy of an emitted photon

You need an infinite amount of time to measure frequency with perfect accuracy. Conversely, an instanteous measurement gives no information about frequency. So the time-span of the measurement needs to be specified before you can say anything about the line-width. Line-width often refers to frequency bandwidth and thus to a range of energies via Planck's constant, h$Delta$f = $Delta$E. The uncertainty principle is usually quoted as $Delta$E. $Delta$T = h/4$pi$. In contrast to the classical position-momentum uncertainty principle, there is less clarity in the interpretation of the energy-time uncertainty.