True.
Surface tension and surface energy per unit area have identical numerical values and identical units because they represent the amount of energy required to increase the surface area of a liquid by a unit amount.
Surface tension is defined as the force per unit length perpendicular to an imaginary line drawn on the surface of a liquid, while surface energy is the amount of energy required to increase the surface area of a liquid by a unit amount.
Since both surface tension and surface energy per unit area are measured in units of force per unit length or energy per unit area, they have identical numerical values and identical units.