Date: 202008
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Flight conditions: Marginal
Weather elements / visibility: Haze / Smoke; 3
Light: Daylight
Aircraft: Cessna 340/340A
Operator: Personal
Operating under: Part 91
Flight plan: IFR
Mission: Personal
Flight phase: Initial Climb
Airspace: Class D ZZZ
Reporter organization: Personal
Reporter function: Single Pilot; Captain; Pilot Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Confusion; Communication Breakdown; Situational Awareness
Second reporter function: Single Pilot; Captain; Pilot Flying
Anomaly: ATC Issue All Types; Conflict Airborne Conflict
Detector: Automation Aircraft RA
Result: General None Reported / Taken
Contributing factors: Human Factors; Procedure; Airspace Structure
Primary problem: Human Factors

Narrative: I received my clearance from the Tower Controller for a VFR climb to IFR. He was hurried and appeared to be irritated. His less than helpful tone and rapid speech was noted as well by the individual sitting in the right front seat who was listening to the conversation. I recall her asking me; 'What was bothering him?'I was holding short of Runway XX at ZZZ. I recall the Controller releasing me for a visual climb to the 'west' and acknowledged. Nothing more specific was stated! Additionally; I was told of an inbound aircraft on the RNAV GPS X or Y; Runway XY approach - I seem to recall a significant distance out; possibly 25 NM. From what I was told; I felt that there was significant time to climb and proceed on my VFR to IFR flight plan without compromise.I made a steep climb of 100 kt. nose high - visibility was limited more than on the ground - as I was concerned and wanted to clear the high terrain to the west ASAP (As Soon As Possible). I followed a course I believed would take me to HLE NDB to the west of the centerline of Runway XX. At what I estimate was about 7000 MSL; I heard the other aircraft report receiving an RA (Resolution Advisory). I looked to my left and saw the other aircraft I estimate to have been 3000+ ft. laterally. He was at my 9 o'clock position at the time and was no factor. I believe he said he saw me as well visually. I reported visual contact to the Controller.With the understanding that the pilot of the other aircraft was following an inbound course of 320 degrees from ZZZZZ; I had to be to the west as he was visualized to my left as noted above. The Controller asked him a question I do not recall after the RA and if he wanted to make the approach from there visually; which was declined by the other pilot. I was then told by the Controller to write down the number of the Tower and call them. He spoke fast. I was in a steep climb with a lower airspeed; nose high; and wanted to avoid the high terrain to my right so I asked him to repeat the number and wrote down [the number]. After I arrived at [State] about 2 hours later; I called; realized I copied the wrong number; and called FSS. He informed me he couldn't tell me their number but when I gave him the number I had; he told me the correction. I called; spoke to [the person]; and gave him my cell phone number; my name; and certificate number. He was not interested in any specifics. He said I would be contacted by the local FSDO.The contributing factors included smoke from many forest fires compromising visibility forward and laterally; a Controller that appeared to have something bothering him; a failure for him to communicate clearly what he meant by flying 'to the west' - centerline; number of miles west; course to accomplish what he expected; my failure to express my concern for terrain as I had not flown into ZZZ1 before - and appreciation that the other aircraft was closer; for whatever reason; than I was led to believe. Finally; it would have been much better for my departure clearance to have been held until the arrival of the incoming aircraft as he was arriving in the opposite direction of my departure with a very narrow passage to and from the runway due to terrain. If the other aircraft had been following the RNAV GPS Y Runway XX approach and had to go missed; he would have turned left directly into my flight path of departure depending on when he began the execution of the missed approach. Fortunately; there was no need for corrective actions. I am not sure of the normal operating procedures at ZZZ1 but for the future; I might suggest that all arrivals and departures be treated as if they are in instrument conditions - or; should either or both arrival and departing aircraft operate under VFR rules; there be a minimum of 5 miles visibility and SKC (Sky Clear) without any weather elements compromising visibility. Thank you for your consideration.


Second narrative: [Report narrative contained no additional information.]


Synopsis: C340 Captain reported an airborne conflict during departure climb-out.