A comprehensive theoretical study of the electronically excited states in complexes between tetracyanoethylene (TCNE) and three aromatic electron donors, benzene, naphthalene and anthracene, was performed with a focus on charge transfer (CT) transitions. The results show that the algebraic diagrammatic construction method to second order (ADC(2)) provides excellent possibilities for reliable calculations of CT states. Significant improvements in the accuracy of the computed transition energies are obtained by using the scaled opposite-spin (SOS) variant of ADC(2). Solvent effects were examined on the basis of the conductor-like screening model (COSMO) which has been implemented recently in the ADC(2) method. The dielectric constant and the refractive index of dichloromethane have been chosen in the COSMO calculations to compare with experimental solvatochromic effects. The computation of optimized ground state geometries and enthalpies of formation has been performed at the second-order Møller-Plesset perturbation theory (MP2) level. By comparison with experimental data and with high-level coupled-cluster methods including explicitly correlated (F12) wave functions, the importance of the SOS approach is demonstrated for the ground state as well. In the benzene-TCNE complex, the two lowest electronic excitations are of CT character whereas in the naphthalene and anthracene TCNE complexes three low-lying CT states are observed. As expected, they are strongly stabilized by the solvent. Geometry optimization in the lowest excited state allowed the calculation of fluorescence transitions. Solvent effects lead to a zero gap between S1 and S0 for the anthracene-TCNE complex. Therefore, in the series of benzene-TCNE to anthracene a change from a radiative to a nonradiative decay mechanism to the ground state is to be expected.