BUG: Fix PeriodIndex +/- TimedeltaIndex
- [x] closes #22998
- [x] tests added / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

Hello @jbrockmendel! Thanks for updating the PR.

 - There are no PEP8 issues in the file [`pandas/core/arrays/datetimelike.py`](https://github.com/jbrockmendel/pandas/blob/e1ebe090bc972a95b436bf28166d1f408fdbe6c5/pandas/core/arrays/datetimelike.py) !

 - There are no PEP8 issues in the file [`pandas/core/arrays/datetimes.py`](https://github.com/jbrockmendel/pandas/blob/e1ebe090bc972a95b436bf28166d1f408fdbe6c5/pandas/core/arrays/datetimes.py) !

 - There are no PEP8 issues in the file [`pandas/core/arrays/period.py`](https://github.com/jbrockmendel/pandas/blob/e1ebe090bc972a95b436bf28166d1f408fdbe6c5/pandas/core/arrays/period.py) !

 - There are no PEP8 issues in the file [`pandas/tests/arithmetic/test_period.py`](https://github.com/jbrockmendel/pandas/blob/e1ebe090bc972a95b436bf28166d1f408fdbe6c5/pandas/tests/arithmetic/test_period.py) !

 - There are no PEP8 issues in the file [`pandas/util/testing.py`](https://github.com/jbrockmendel/pandas/blob/e1ebe090bc972a95b436bf28166d1f408fdbe6c5/pandas/util/testing.py) !

 - Complete extra results for this file :

> file_to_check.py:2456:-258: W605 invalid escape sequence '\('
file_to_check.py:2456:-255: W605 invalid escape sequence '\)'
---



##### Comment last updated on October 09, 2018 at 23:56 Hours UTC # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23031?src=pr&el=h1) Report
> Merging [#23031](https://codecov.io/gh/pandas-dev/pandas/pull/23031?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/f6da1f1ec3b68a9210be158a693ac389076fa179?src=pr&el=desc) will **decrease** coverage by `0.05%`.
> The diff coverage is `85%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/23031/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/23031?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #23031      +/-   ##
==========================================
- Coverage   92.19%   92.14%   -0.06%     
==========================================
  Files         169      170       +1     
  Lines       50911    51103     +192     
==========================================
+ Hits        46939    47087     +148     
- Misses       3972     4016      +44
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.56% <85%> (-0.06%)` | :arrow_down: |
| #single | `42.27% <15%> (-0.04%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/23031?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/arrays/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lcy5weQ==) | `96.94% <ø> (+0.02%)` | :arrow_up: |
| [pandas/util/testing.py](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvdGVzdGluZy5weQ==) | `86.45% <100%> (+0.26%)` | :arrow_up: |
| [pandas/core/arrays/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lbGlrZS5weQ==) | `94.89% <60%> (-0.67%)` | :arrow_down: |
| [pandas/core/arrays/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3BlcmlvZC5weQ==) | `95.56% <87.87%> (+2.71%)` | :arrow_up: |
| [pandas/core/ops.py](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvb3BzLnB5) | `94.39% <0%> (-2.8%)` | :arrow_down: |
| [pandas/compat/numpy/function.py](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree#diff-cGFuZGFzL2NvbXBhdC9udW1weS9mdW5jdGlvbi5weQ==) | `86.66% <0%> (-1.82%)` | :arrow_down: |
| [pandas/core/dtypes/concat.py](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZHR5cGVzL2NvbmNhdC5weQ==) | `97.69% <0%> (-1.49%)` | :arrow_down: |
| [pandas/core/internals/concat.py](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzL2NvbmNhdC5weQ==) | `96.83% <0%> (-1.17%)` | :arrow_down: |
| [pandas/core/internals/managers.py](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzL21hbmFnZXJzLnB5) | `95.77% <0%> (-0.9%)` | :arrow_down: |
| [pandas/core/internals/blocks.py](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzL2Jsb2Nrcy5weQ==) | `92.91% <0%> (-0.58%)` | :arrow_down: |
| ... and [37 more](https://codecov.io/gh/pandas-dev/pandas/pull/23031/diff?src=pr&el=tree-more) | |

------

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> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23031?src=pr&el=footer). Last update [f6da1f1...ed50b9f](https://codecov.io/gh/pandas-dev/pandas/pull/23031?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 Updated with a whatsnew and more tests.  Doing this right required more a refactor than I expected, but in the end it touches only arithmetic code and doesn't fiddle with indexing code (like the previous attempt did) gentle ping lgtm. just add a couple of comments. merge when green Ping