Welcome to the RStudio community!
The Java error can be annoying and many people at some point run into issues with it.
First of all, have you installed Java? If not, do that first (this is not an R package, but separate software):
Then install rJava too in R:
Then try again.
Second, I don't know DEA, but installing the rDEA package and running the example it seems that a DEA object is a list and not a data frame. You can't write list like that to excel, or transform it into a data frame. You need to parse the different parts of the list into a dataframe manually (meaning coding it yourself) then save it.
Having said that, I see that the lists have similar lengths, so it actually is possible writing it to excel without extra transformations (though all will be put together in one sheet). Here is an example (taken from the package's examples):
## inputs and outputs for analysis
Y = hospitals[c('inpatients', 'outpatients')]
X = hospitals[c('labor', 'capital')]
W = hospitals[c('labor_price', 'capital_price')]
## Naive input-oriented DEA score for the first 20 firms under variable returns-to-scale
di_naive = dea(XREF=X, YREF=Y, X=X[firms,], Y=Y[firms,], model="input", RTS="variable")
Hope this helps,