ΔE 37.5, loose: different enough that you should pick on purpose. Cardinal Purple is a little lighter, much more saturated, cooler than Radiant Orange.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 38). Cardinal Purple is a little lighter, much more saturated, cooler than Radiant Orange.
The same difference applies the other way round: Radiant Orange is a little darker, much more muted, warmer.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Radiant Orange on the colour wheel See Cardinal Purple on the colour wheel
All matches: Radiant Orange equivalents · Cardinal Purple equivalents