"Background: Shape coexistence in heavy nuclei poses a strong challenge to state-of-the-art nuclear models, where several competing shape minima are found close to the ground state. A classic region for investigating this phenomenon is in the region around Z = 82 and the neutron midshell at N = 104. Purpose: Evidence for shape coexistence has been inferred from a-decay measurements, laser spectroscopy, and in-beam measurements. While the latter allow the pattern of excited states and rotational band structures to be mapped out, a detailed understanding of shape coexistence can only come from measurements of electromagnetic matrix elements. Method: Secondary, radioactive ion beams of Rn-202 and Rn-204 were studied by means of low-energy Coulomb excitation at the REX-ISOLDE in CERN. Results: The electric-quadrupole (E2) matrix element connecting the ground state and first excited 2(1)(+) state was extracted for both Rn-202 and Rn-204, corresponding to B(E2; 2(1)(+) -> 0(1)(+)) = 29(-8)(+8) and 43(-12)(+17) W.u., respectively. Additionally, E2 matrix elements connecting the 2(1)(+) state with the 4(1)(+) and 2(2)(+) states were determined in Rn-202. No excited 0(+) states were observed in the current data set, possibly owing to a limited population of second-order processes at the currently available beam energies. Conclusions: The results are discussed in terms of collectivity and the deformation of both nuclei studied is deduced to be weak, as expected from the low-lying level-energy schemes. Comparisons are also made to state-of-the-art beyond-mean-field model calculations and the magnitude of the transitional quadrupole moments are well reproduced."