Sorting problems R dataframe

I'm having trouble with sorting my dataframe in R.
It is a large dataframe in which there is 1 variable (the mean absolute deviation), referred to as mads as the columnname
There are more than 300.000 rows in which every row has a seperate name.
I want to order the mean absolute deviation is descending order, but also contain the corresponding rowname.
I only succeed in receiving the descending order but losing the corresponding row name.

library(tidyverse)

#construct example data

set.seed(42)

#inventing mads
example_data <- data.frame(mads =  runif(300000,0,1))

#inventing rownames
rn_to_use <- head(combn(x = c(LETTERS,letters,0:9),m = 4,simplify = FALSE),n=300000) %>%
  map_chr(~paste0(.,collapse=""))

rownames(example_data) <- rn_to_use

#solution

arrange(example_data,desc(mads))

Hope the above helps.
As you can see preparing an example took me more effort than solving for what you want...

in the future you could provide representative data. the R package datapasta has wonderful functions for that.
for example the first 20records from the data I used could have been generated and shared here like so :

datapasta::df_paste(head(example_data,20))

this provides the text:

data.frame(
   row.names = c("ABCD","ABCE","ABCF","ABCG","ABCH",
                 "ABCI","ABCJ","ABCK","ABCL","ABCM","ABCN","ABCO","ABCP",
                 "ABCQ","ABCR","ABCS","ABCT","ABCU","ABCV","ABCW"),
        mads = c(0.914806043496355,0.937075413297862,
                 0.286139534786344,0.830447626067325,0.641745518893003,
                 0.519095949130133,0.736588314641267,0.13466659723781,0.656992290401831,
                 0.705064784036949,0.45774177624844,0.719112251652405,
                 0.934672247152776,0.255428824340925,0.462292822543532,
                 0.940014522755519,0.978226428385824,0.117487361654639,0.474997081561014,
                 0.560332746244967)

Which could form the data part of reprex



library(tidyverse)

example_data <- data.frame(
  row.names = c("ABCD","ABCE","ABCF","ABCG","ABCH",
                "ABCI","ABCJ","ABCK","ABCL","ABCM","ABCN","ABCO","ABCP",
                "ABCQ","ABCR","ABCS","ABCT","ABCU","ABCV","ABCW"),
  mads = c(0.914806043496355,0.937075413297862,
           0.286139534786344,0.830447626067325,0.641745518893003,
           0.519095949130133,0.736588314641267,0.13466659723781,0.656992290401831,
           0.705064784036949,0.45774177624844,0.719112251652405,
           0.934672247152776,0.255428824340925,0.462292822543532,
           0.940014522755519,0.978226428385824,0.117487361654639,0.474997081561014,
           0.560332746244967)

#solution

arrange(example_data,desc(mads))