Join two data tables and use only one column from second dt

data.table solution

setDT(dt1)[ , H := dt2$H[match(dt1$A , dt2$E)] , ]

#    A  B  C  H
# 1: 1  4  7 16
# 2: 2  5  8 17
# 3: 3  6  9 18
# 4: 2 20 21 17

another dplyr solution will be

left_join(x = dt1 , y = dt2 , by = c("A" = "E")) %>% 
select(one_of(c("A" , "B" , "C" , "H")))

In order to perform a left join to df1 and add H column from df2, you can combine binary join with the update by reference operator (:=)

setkey(setDT(dt1), A) 
dt1[dt2, H := i.H]

See here and here for detailed explanation on how it works

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With the devel version (v >= 1.9.5) we could make it even shorter by specifying the key within setDT (as pointed by @Arun)

setDT(dt1, key = "A")[dt2, H := i.H]

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Edit 24/7/2015

You can now run a binary join using the new on parameter without setting keys

setDT(dt1)[dt2, H := i.H, on = c(A = "E")]