We study intact and bulging Escherichia coli cells using atomic force microscopy to separate the contributions of the cell wall and turgor pressure to the overall cell stiffness. We find strong evidence of power-law stress stiffening in the E. coli cell wall, with an exponent of 1.22±0.12, such that the wall is significantly stiffer in intact cells (E=23±8  MPa and 49±20  MPa in the axial and circumferential directions) than in unpressurized sacculi. These measurements also indicate that the turgor pressure in living cells E. coli is 29±3  kPa.