Distance between UTM coordinates

I have points on a QGIS map, and want to determine the distance between each of the points in R. Each Unique ID is a tree. The coordinates are UTM coordinates (x = East, y = North)

My dataset looks like this:

What formula would I use so I can get an output that describes the distance between each tree, looking like this (where x is the distance between each tree):

Or perhaps if it is more simple, repeated rows (e.g. 45 against 49, 45 against 70, 45 against 71; and etc. with each repetition being a new row)

With tidyverse and sf, and to get the distance matrix in meters, try:

library(tidyverse)
library(sf)

df <- tibble(
   Unique_ID = c(45L, 49L, 70L, 71L),
        EW_X = c(573500L, 572224L, 573573L, 573573L),
        EW_Y = c(775011L, 774700L, 775200L, 775200L))

sf_trees <- st_as_sf(x = df, coords = c("EW_X", "EW_Y"),
                     crs = 3857) # Note that I am using WGS 84 Pseudo Mercator. If you know the UTM zone you could be more specific with the csr/epsg code
tb_distance <- st_distance(sf_trees, sf_trees, ) %>%  # The following 3 lines are optional.
  as_tibble() %>% 
  set_names(nm = df$Unique_ID) %>% 
  bind_cols(tibble(Unique_ID = as.character(df$Unique_ID)), . )

tb_distance
# A tibble: 4 x 5
  Unique_ID  `45`  `49`  `70`  `71`
  <chr>       [m]   [m]   [m]   [m]
1 45           0  1313.  203.  203.
2 49        1313.    0  1439. 1439.
3 70         203. 1439.    0     0 
4 71         203. 1439.    0     0