The shovel operator << performs much better than += when dealing with long strings because the shovel operator is allowed to modify the original string, whereas += has to copy all the text from the first string into a new string every time it runs.
There is no += operator defined on the String class, because += is a combined operator. In short x += "asdf" is exactly equivalent to x = x + "asdf", so you should reference the + operator on the string class, not look for a += operator.