split character data into numbers and letters

For your regex you have to use:

gsub("[[:digit:]]","",my.data)

The [:digit:] character class only makes sense inside a set of [].

With stringr, if you like (and slightly different from the answer to the other question):

# load library
library(stringr)
#
# load data
my.data <- c("aaa", "b11", "b21", "b101", "b111", "ccc1", "ddd1", "ccc20", "ddd13")
#
# extract numbers only
my.data.num <- as.numeric(str_extract(my.data, "[0-9]+"))
#
# check output
my.data.num
[1]  NA  11  21 101 111   1   1  20  13
#
# extract characters only
my.data.cha <- (str_extract(my.data, "[aA-zZ]+"))
# 
# check output
my.data.cha
[1] "aaa" "b"   "b"   "b"   "b"   "ccc" "ddd" "ccc" "ddd"

Since none of the previous answers use tidyr::separate here it goes:

library(tidyr)

df <- data.frame(mycol = c("APPLE348744", "BANANA77845", "OATS2647892", "EGG98586456"))

df %>%
  separate(mycol, 
           into = c("text", "num"), 
           sep = "(?<=[A-Za-z])(?=[0-9])"
           )