From the first rules, it seems clear that the angle brackets are
metasyntactic parenthesis used to denote Kleene closure over more than
a single symbol. This is also suggested by the existence of normal
brackets in the grammar. This also suggest that the example rule for $E$ is
syntactically not well formed and means nothing at all, since the star
cannot apply to a metasyntactic parenthesis (as the first star seems
to be doing). The correct rule is probably: $E \to T \langle +T\rangle^*$
and the corresponding parser:
proc E begin
while symbol='+' do
Generating a parser for $\langle A \rangle$ is just generating a
parser for $A$ alone. The angle brackets are just grammatical notation
(like the arrow or the vertical bar), and are not supposed to appear
in generated strings.
They are not necessary here, but could be if you had Kleene star over
several symbols, such as $\langle AB \rangle^*$, as in my corrected version of the rule for $E$.
With these corrections, you should be able to finish your recursive descent parser.