The electric quadrupole transition from the first 2+ state to the ground 0+ state in 18C was studied through lifetime measurement by an upgraded recoil shadow method applied to inelastically scattered radioactive 18C nuclei. The measured mean lifetime is 18.9 +/- 0.9 (stat) +/- 4.4 (syst) ps, corresponding to a B(E2;2+ -> 0+) value of 4.3 +/- 0.2 +/- 1.0 e2fm4, or about 1.5 Weisskopf units. The mean lifetime of the first 2+ state in 16C was remeasured to be 18.0 +/- 1.6 +/- 4.7 ps, about four times shorter than the value reported previously. The discrepancy between the two results was resolved by incorporating the gamma-ray angular distribution measured in this work into the previous measurement. These transition strengths are hindered compared to the empirical transition strengths, indicating that the anomalous hindrance observed in 16C persists in 18C. ; Comment: Submitted to Physical Review C; 26 pages with 13 figures