diff --git a/lib/dentaku/date_arithmetic.rb b/lib/dentaku/date_arithmetic.rb
index 72fddb4..3b81477 100644
--- a/lib/dentaku/date_arithmetic.rb
+++ b/lib/dentaku/date_arithmetic.rb
@@ -29,7 +29,7 @@ def add(duration)
 
     def sub(duration)
       case duration
-      when DateTime, Numeric
+      when Date, DateTime, Numeric
         @base - duration
       when Dentaku::AST::Duration::Value
         case duration.unit
@@ -40,6 +40,8 @@ def sub(duration)
         when :day
           @base - duration.value
         end
+      when Dentaku::TokenScanner::DATE_TIME_REGEXP
+        @base - Time.parse(duration).to_datetime
       else
         raise Dentaku::ArgumentError.for(:incompatible_type, value: duration, for: Numeric),
           "'#{duration || duration.class}' is not coercible for date arithmetic"
diff --git a/lib/dentaku/token_scanner.rb b/lib/dentaku/token_scanner.rb
index eb7e15a..5770993 100644
--- a/lib/dentaku/token_scanner.rb
+++ b/lib/dentaku/token_scanner.rb
@@ -7,7 +7,7 @@ module Dentaku
   class TokenScanner
     extend StringCasing
 
-    DATE_TIME_REGEXP = /\d{2}\d{2}?-\d{1,2}-\d{1,2}( \d{1,2}:\d{1,2}:\d{1,2})? ?(Z|((\+|\-)\d{2}\:?\d{2}))?(?!\d)/.freeze
+    DATE_TIME_REGEXP = /\d{2}\d{2}?-\d{1,2}-\d{1,2}([ |T]\d{1,2}:\d{1,2}:\d{1,2}(\.\d*)?)? ?(Z|((\+|\-)\d{2}\:?\d{2}))?(?!\d)/.freeze
 
     def initialize(category, regexp, converter = nil, condition = nil)
       @category  = category
diff --git a/spec/calculator_spec.rb b/spec/calculator_spec.rb
index d6906ed..b7ef8cf 100644
--- a/spec/calculator_spec.rb
+++ b/spec/calculator_spec.rb
@@ -471,16 +471,20 @@
 
     it 'from string variable' do
       value = '2023-01-01'
+      value2 = '2022-12-31'
 
-      expect(calculator.evaluate!('value + duration(1, month)', { value: value }).to_date).to eql(Date.parse('2023-02-01'))
-      expect(calculator.evaluate!('value - duration(1, month)', { value: value }).to_date).to eql(Date.parse('2022-12-01'))
+      expect(calculator.evaluate!('value + duration(1, month)', { value: value }).to_date).to eq(Date.parse('2023-02-01'))
+      expect(calculator.evaluate!('value - duration(1, month)', { value: value }).to_date).to eq(Date.parse('2022-12-01'))
+      expect(calculator.evaluate!('value - value2', { value: value, value2: value2 })).to eq(1)
     end
 
     it 'from date object' do
       value = Date.parse('2023-01-01').to_date
+      value2 = Date.parse('2022-12-31').to_date
 
-      expect(calculator.evaluate!('value + duration(1, month)', { value: value }).to_date).to eql(Date.parse('2023-02-01'))
-      expect(calculator.evaluate!('value - duration(1, month)', { value: value }).to_date).to eql(Date.parse('2022-12-01'))
+      expect(calculator.evaluate!('value + duration(1, month)', { value: value }).to_date).to eq(Date.parse('2023-02-01'))
+      expect(calculator.evaluate!('value - duration(1, month)', { value: value }).to_date).to eq(Date.parse('2022-12-01'))
+      expect(calculator.evaluate!('value - value2', { value: value, value2: value2 })).to eq(1)
     end
   end
 
diff --git a/spec/tokenizer_spec.rb b/spec/tokenizer_spec.rb
index ac5d562..962cc32 100644
--- a/spec/tokenizer_spec.rb
+++ b/spec/tokenizer_spec.rb
@@ -1,3 +1,4 @@
+require 'dentaku/exceptions'
 require 'dentaku/tokenizer'
 
 describe Dentaku::Tokenizer do
@@ -234,9 +235,9 @@
   end
 
   it 'tokenizes Time literals' do
-    tokens = tokenizer.tokenize('2017-01-01 2017-01-2 2017-1-03 2017-01-04 12:23:42 2017-1-5 1:2:3 2017-1-06 1:02:30 2017-01-07 12:34:56 Z 2017-01-08 1:2:3 +0800')
-    expect(tokens.length).to eq(8)
-    expect(tokens.map(&:category)).to eq([:datetime, :datetime, :datetime, :datetime, :datetime, :datetime, :datetime, :datetime])
+    tokens = tokenizer.tokenize('2017-01-01 2017-01-2 2017-1-03 2017-01-04 12:23:42 2017-1-5 1:2:3 2017-1-06 1:02:30 2017-01-07 12:34:56 Z 2017-01-08 1:2:3 +0800 2017-01-08T01:02:03.456Z')
+    expect(tokens.length).to eq(9)
+    expect(tokens.map(&:category)).to eq([:datetime, :datetime, :datetime, :datetime, :datetime, :datetime, :datetime, :datetime, :datetime])
     expect(tokens.map(&:value)).to eq([
       Time.local(2017, 1, 1).to_datetime,
       Time.local(2017, 1, 2).to_datetime,
@@ -245,7 +246,8 @@
       Time.local(2017, 1, 5, 1, 2, 3).to_datetime,
       Time.local(2017, 1, 6, 1, 2, 30).to_datetime,
       Time.utc(2017, 1, 7, 12, 34, 56).to_datetime,
-      Time.new(2017, 1, 8, 1, 2, 3, "+08:00").to_datetime
+      Time.new(2017, 1, 8, 1, 2, 3, "+08:00").to_datetime,
+      Time.utc(2017, 1, 8, 1, 2, 3, 456000).to_datetime
     ])
   end