Basically here we are making an equation and evaluating it.

library("dplyr")
library(stringr)
#fetching varaible names and forming an equation
equation_<- paste0(collapse = "+",str_subset(colnames(mtcars),"[a-z]"))
#using mutate function parsing and evaluating the equation to the result
mtcars %>% mutate(Sum_Col=eval(parse(text=equation_)))