We examine energy efficiency in the European Union (EU) using an integrated model that connects labor and capital as production factors with energy consumption to produce GDP with a limited amount of environmental emissions. The model is a linear output-oriented BCC data envelopment analysis (DEA) that employs variables with non-negative values to calculate efficiency scores for a sample of 28 EU member states in the period 2010−2018. We assume variable returns to scale (VRS) considering the natural inclination of countries to adopt technologies that allow them to produce higher outputs over extended periods of time, which we observed through the trends of increasing labor productivity and decreasing energy intensity over the analyzed period. The average EU inefficiency margin in the sample period is 16.0%, with old member states being significantly more efficient (4.2%) than new member states (29.5%). Energy efficiency management does not improve over time, especially in new member states that had substantially worse efficiency by 2018 than in 2010. New member states could increase energy efficiency through the liberalization of the energy market, the support of energy-saving and technologically advanced industries, and the introduction of measures aimed at increasing the productivity levels in the economy.