Regular Expression with +/-

lst = {"Today+100", "Yesterday-200"};

StringSplit

StringSplit[lst, RegularExpression["([+-]\\d+)"] :> ToExpression@"$1"]

{{"Today", 100}, {"Yesterday", -200}}

StringSplit[lst, n : NumberString :> ToExpression@n]

{{"Today", 100}, {"Yesterday", -200}}

StringReplace

List @@@ StringReplace[lst, RegularExpression["([+-]\\d+)"] :> ToExpression@"$1"]

List @@@ StringReplace[lst, n : NumberString :> ToExpression@n]

Sequence @@@ StringReplace[lst,
   RegularExpression["(\\w+)([+-]\\d+)"] :> {"$1", ToExpression@"$2"}]

Sequence @@@ StringReplace[lst, 
  w : WordCharacter .. ~~ n : NumberString :> {w, ToExpression @ n}]

all give

{{"Today", 100}, {"Yesterday", -200}}

Note: My original answer used the regex substring [\\+\\-]. I learned from @user1066's comment and answer that it can be replaced with much nicer [+-].

Maybe this will help:

StringCases[#, 
    WordCharacter .. | (_ ~~ DigitCharacter ..)] & /@ {"Today+100", 
   "Yesterday-200"} // Flatten
(* {"Today", "+100", "Yesterday", "-200"} *)

A slight modification of @kglr's first method, (the one containing the neat use of ToExpression):

StringSplit[lst, 
  RegularExpression["[+-]\d{3}"]:> ToExpression["$0"]]

{{Today, 100}, {Yesterday, -200}}

(Originally posted as a comment)