Observed spectra of R Coronae Borealis (RCB) and hydrogen-deficient carbon (HdC) stars are analyzed by synthesizing the C_2_ Swan bands (1, 0), (0, 0), and (0, 1) using our detailed line list and the Uppsala model atmospheres. The (0, 1) and (0, 0) C_2_ bands are used to derive the ^12^C abundance, and the (1, 0) ^12^C^13^C band to determine the ^12^C/^13^C ratios. The carbon abundance derived from the C_2_ Swan bands is about the same for the adopted models constructed with different carbon abundances over the range 8.5 (C/He=0.1%) to 10.5 (C/He=10%). Carbon abundances derived from C I lines are about a factor of four lower than the carbon abundance of the adopted model atmosphere over the same C/He interval, as reported by Asplund et al., who dubbed the mismatch between adopted and derived C abundance as the "carbon problem." In principle, the carbon abundances obtained from C_2_ Swan bands and that assumed for the model atmosphere can be equated for a particular choice of C/He that varies from star to star. Then, the carbon problem for C_2_ bands is eliminated. However, such C/He ratios are in general less than those of the extreme helium stars, the seemingly natural relatives to the RCB and HdC stars. A more likely solution to the C_2_ carbon problem may lie in a modification of the model atmosphere's temperature structure. The derived carbon abundances and the ^12^C/^13^C ratios are discussed in light of the double degenerate and the final flash scenarios.