Extreme Ultraviolet Explorer (EUVE) data of two active solar analogs, 47 Cas and EK Dra, were used to investigate flare statistics and the distribution of the flare occurrence rate in energy. The EUVE satellite observed each star for almost 7 days. Simultaneous spectral data from its spectrometers were used to derive temperature and abundance characteristics of their coronae. The emission models were derived from differential emission measure distributions by fitting optically thin thermal models to the spectra. The Deep Survey instrument photon lists were analyzed by applying different time binnings. A total of 28 flares were identified for further analysis. The timing study provided estimates for the total radiative energy loss of each flare. The differential distribution of flares in total X-ray energy is found to be a power law (dN/dEE^−α, with α≈2.2±0.2) valid in the energy range between 3×10³³ and 6×10³⁴ ergs. The power-law index is larger than that for typical solar flares but is similar to indices found recently for small-scale solar events. If the power law continues to energies of moderate solar flares, then the total energy emitted by the ensemble of all flares may suffice to explain all of the observed flaring and "quiescent" X-ray emissions of the two stars. A considerable portion, if not all, of the energy required to heat their coronae could thus be provided by flares.