NCERT (periodic properties) says that if electron is added and energy released then electron gain enthalpy is negative. On the next page the same statement is given for electron affinity also. But EA and EGE are negative of each other , so which one will have -ve sign when energy is released?

Electron gain enthalpy is sometimes also referred to as Electron Affinity  although there is a minute difference between them. Electron gain enthalpy is defined as the amount of energy released when an electron is added to an isolated gaseous atom. During the addition of an electron, energy can either be released or absorbed.

Sign Convention For Electron Gain Enthalpy:

Negative: When energy is released while accepting an electron.

Positive: When energy is supplied to an atom while adding an electron.