This is (surprisingly) not trivial. There is Macro for week number but the implementation there seems to be slightly unreliable. If you are willing to use LuaLaTeX then you can make a system call to find the week number (and other parts of the date).
Note that the system library defines Sunday as 0, while ISO 8601 defines it as 7.
MWE:
\documentclass{article}
\usepackage{luacode}
\newcommand{\weektoday}{\printdate{\the\year}{\the\month}{\the\day}}
\newcommand{\printdate}[3]{%
\luaexec{
timestamp = os.time{year=#1, month=#2, day=#3}
daynr = os.date("\%w",timestamp)
if daynr == "0" then daynr = "7" end
tex.sprint(os.date("\%YW\%V-",timestamp)..daynr)
}
}
\begin{document}
Today: \weektoday
Other date: \printdate{2018}{3}{4}
\end{document}
Result:

Compatibility note: on Windows the %V
format is not implemented. Instead you can use %U
(first Sunday starts week 0) or %W
(first Monday starts week 0), however both are different from the ISO standard (first Thursday determines week 1). You can calculate the ISO week number manually in Lua but in that case you may just as well use a pure LaTeX solution.
W083
?