Here's what matters: you don't need to parse the string carefully. Just collect all the digit characters into a vector and ignore the plus signs. Then sort the digits. I'll show you how.
Loop through each character in the string. If it's a digit (not a plus sign), add it to your vector. After the loop, you'll have all numbers without the operators. This pattern works for any problem where you need to filter and rearrange parts of a string.
Separate data from structure, process the data, then rebuild the structure.